NationStates Jolt Archive

i know 0 is neither negitive or positive but what about odd/even i think its even

odd nimbers start at 1 and go every other number 1,3,5,7;1,-1,-3,-5,-7
even starts at 2 and go every other number 2,4,6,8;2,0,-2,-4,-6,-8

zero is not a number, is is a word.

Odd.

Division of zero by 2 or -2 does not give a number of the N-family.

Odd poll though.

public boolean isEven (int n)
{
if (n % 2 == 0)
return true;
else return false;
}

isEven(0) returns true.

Even most of the time.

An even integer is if it can be written in the form of 2N where N is some integer.

Another way is to say there is no remainder when divided by 2.

An odd integer can be written in the form of 2N + 1.

Obviously an odd integer leaves a remainder when divied by two.

So under this definition, zero is clearly even since 0/2 = 0 with no remainder.

In order for something to be either odd or even, it must have value. Zero is defined as the absence of value, therefore it is neither odd nor even.

Neither; because dividing it by both an odd and an even number will still get you 0

Neither. In order for a number to be odd or even it must actually be a number, and since the symbol 0 represents the *absence* of a number it can't be either odd or even. That's also why a number divided by zero equals that number, it's just a fancy way to say that the number in question isn't being divided.

In order for something to be either odd or even, it must have value. Zero is defined as the absence of value, therefore it is neither odd nor even.
that's what i said.

Even most of the time.

An even integer is if it can be written in the form of 2N where N is some integer.

Another way is to say there is no remainder when divided by 2.

An odd integer can be written in the form of 2N + 1.

Obviously an odd integer leaves a remainder when divied by two.

So under this definition, zero is clearly even since 0/2 = 0 with no remainder.


Sorry, but N-family does NOT include zero, no more than it includes negatives.
N is not integer, N is natural numbers ( 1, 2, 3... infinity-1 ).

Neither - the value zero is neutral

Zero is not the absence of value, zero is a value of zero, all the mathmeticians i know say zero is even

According to my foundations of math classes; zero is even. Linguisitically, anger and mortality is probably right.

It is neutral, but if you must assign somehting it is even. Any number times two is zero. 0 x 2 = 0 :: 0 is even

Sorry, but N-family does NOT include zero, no more than it includes negatives.
N is not integer, N is natural numbers ( 1, 2, 3... infinity-1 ).

Ok bad choice call it an int and the fact remains.

A source for another explantion:

http://mathforum.org/library/drmath/view/57104.html

after having a university professor who would take away a lot of points for making the mistake of calling 0 an integer, it's neither.

0 is even.

Work it out this way:

even + even = even
2 + 2 = 4
0 + 2 = 2

odd + even = odd
2 + 3 = 5
0 + 3 = 3

odd + odd = even
3 + 3 = 6
-1 + 1 = 0

Ok bad choice call it an int and the fact remains.

A source for another explantion:

http://mathforum.org/library/drmath/view/57104.html


Odd and Even are concepts that only apply to N-family in first place..
:D

Who Cares

I'm standing by Dunbarrow's side on this one i see.

to interrupt your thread, but i have a burning off topic question and the thread starter won't work: There is a song with a Van Halen-eque guitar riff at its end and a repeated riff that sounds more like Jimi Hendrix. The drumming is pretty heavy and the voice isn't that distinctive. Its sounds pretty old, but i heard it on an altrock station. Does anyone have any idea who it might be? (I couldn't really catch the lyrics.) Again, sorry...

Well, since 99.9% of the time we can assume that we are dealing with the set of integers, zero is even. In the relatively rare event (after the third grade) that we are restricting our mathematics to the natural numbers, the correct answer is "neither."

An integer N is even if it can be expressed as 2n, where n is any integer. 0=2(0). Even.

(You will also notice that the even integers make a very nice algebraic ring only if we include zero in the set. It is therefore convenient to do so.)

That's also why a number divided by zero equals that number, it's just a fancy way to say that the number in question isn't being divided.

A number divided by zero = does not compute. As a programmer, I will stick to the fact that zero is even, for sanity's sake.

It is merely a placeholder.

A number divided by zero = does not compute. As a programmer, I will stick to the fact that zero is even, for sanity's sake.


Programmers are to mathematicians what engineers are to scientists...
( i.e. the rather clueless blue collar workers )
*hides from very angry mod*

Ok bad choice call it an int and the fact remains.

A source for another explantion:

http://mathforum.org/library/drmath/view/57104.html1

zero is clearly even since 0/2 = 0 with no remainder.

But you can't divide 0 by any interger. 0/n is undefined no matter what n stands for.

even: All other numbers ending with zero are even

Odd.

Division of zero by 2 or -2 does not give a number of the N-family.

And you have never heard the expression "an even integer"? The qualities "odd" and "even" are certainly defined on the set of integers, of which 0 is a member. If the set is restricted to natural numbers, zero is neither odd nor even. Otherwise it is even, since 2(0)=0.

A number divided by zero = does not compute. As a programmer, I will stick to the fact that zero is even, for sanity's sake.
A number divided by zero is infinite.

But you can't divide 0 by any interger. 0/n is undefined no matter what n stands for.

0 / n = 0

n / 0 on the other hand is undefined

after having a university professor who would take away a lot of points for making the mistake of calling 0 an integer, it's neither.

If he did, he should have his Ph.D. revoked! Zero is certainly an integer! Hence the need for that occasional reminder that some problems specify a "non-zero integer." That would be a bit redundant if zero were not an integer.

And you have never heard the expression "an even integer"? The qualities "odd" and "even" are certainly defined on the set of integers, of which 0 is a member. If the set is restricted to natural numbers, zero is neither odd nor even. Otherwise it is even, since 2(0)=0.

My point is that integers and N are NOT equal. N is a subset of integers. You cannot extrapolate N-rules to INT-family. Odd and even refer to N, not int.

If you beg to differ, I challenge you to construct a space with -1 dimensions.
Have fun.

http://ns.goobergunch.net/GeneralForum.java
http://ns.goobergunch.net/GeneralForum.class

Enjoy.

But you can't divide 0 by any interger. 0/n is undefined no matter what n stands for.

No, n/0 is undefined. 0/n=0. Just multiply both sides by n and see.

A number divided by zero is infinite.

Technically, it's undefined.

http://ns.goobergunch.net/GeneralForum.java
http://ns.goobergunch.net/GeneralForum.class

Enjoy.

*refers goobergunchia to his post on the relation between programmers and mathematicians*

0 / n = 0

n / 0 on the other hand is undefined

sorry :D
I got them mixed up.

*refers goobergunchia to his post on the relation between programmers and mathematicians*

Let's take a look at the work accomplished by programmers and matematicians, shall we? Programmers made all of this possible. Mathematicians spend seven years in solitude to try and prove Fermat's last theorem(x^3 + y^3 does not equal z^3)...and then realize their proof is wrong.

My point is that integers and N are NOT equal.

Yes, so?

N is a subset of integers.
Yep.
You cannot extrapolate N-rules to INT-family.
No one is trying to.
Odd and even refer to N, not int.

That's where you are wrong. Even integers are quite well defined, as any integer that can be expressed in the form 2n. Check any math book. Occasionally one may want to work only in N, but because it is not closed on addition (e.g. the equation x+5=3 has no solution) mathematicians almost always use the set of integers, Z. (When doing this sort of number theory... obviously, the reals and complex numbers, or the rational numbers, all have plenty of lovely applications.)

If you beg to differ, I challenge you to construct a space with -1 dimensions.

That has nothing to do with this conversation. Does this nonsense usually impress people?

Let's take a look at the work accomplished by programmers and matematicians, shall we? Programmers made all of this possible. Mathematicians spend seven years in solitude to try and prove Fermat's last theorem(x^3 + y^3 does not equal z^3)...and then realize their proof is wrong.

Fermat's last theorem was x^n+y^n /= z^n for n > 2. and actually it's proven correct.

Yes, so?


Yep.

No one is trying to.


That's where you are wrong. Even integers are quite well defined, as any integer that can be expressed in the form 2n. Check any math book. Occasionally one may want to work only in N, but because it is not closed on addition (e.g. the equation x+5=3 has no solution) mathematicians almost always use the set of integers, Z.



That has nothing to do with this conversation. Does this nonsense usually impress people?


Yes, you are. It is the fine point of it. Odd and Even only apply to N. Not to Z. Notwithstanding math-books for beginners.
I'm still waiting for you to try to construct any space of -1 dimension.

I didn't read all of the other argument's but from what i know 0 is nuetral

Yes, you are. It is the fine point of it. Odd and Even only apply to N. Not to Z. Notwithstanding math-books for beginners.
I'm still waiting for you to try to construct any space of -1 dimension.

If odd/even only applies to N does that mean that -2 is neither odd nor even? or any negative number for that matter?

Yes, you are. It is the fine point of it. Odd and Even only apply to N. Not to Z. Notwithstanding math-books for beginners.

Really? Fine then... Quote me a math book--any math book of your choosing--that says that odd and even apply to N, but not Z.

And while you're at it, count how many times you read the words "even integer" or "odd integer."

I'm still waiting for you to try to construct any space of -1 dimension.

Again, why?? When the challenge has no relation to the discussion?? Seriously, indulge my curiosity. Explain the connection.

Secondly, we both already know that's nonsense.

Really? Fine then... Quote me a math book--any math book of your choosing--that says that odd and even apply to N, but not Z.

And while you're at it, count how many times you read the words "even integer" or "odd integer."



Again, why?? When the challenge has no relation to the discussion?? Seriously, indulge my curiosity. Explain the connection.

Secondly, we both already know that's nonsense.

*snarls* familiar with Lobachevski or Boljay?

Fermat's last theorem was x^n+y^n /= z^n for n > 2. and actually it's proven correct.

Yeah, it was after about 7 years of work in solitary. And then it still took a few more months to correct the proof. Either way, it's a rather useless proof.

*refers goobergunchia to his post on the relation between programmers and mathematicians*

*refers Dunbarrow to his 5s on AP Calculus and AP Computer Science tests* :P

On a related note, I have determined that writing a function to approximate the Riemann zeta function was a mistake, given that it's been working on RiemannZeta(3.0) for about ten minutes now and there's still no sign of an answer.

*snarls* familiar with Lobachevski or Boljay?

Clearly you know the texts so well, you must have a copy of something lying around. I need editions and page numbers so I can head to the library and verify this mysterious finding.

Pretty please?

If odd/even only applies to N does that mean that -2 is neither odd nor even? or any negative number for that matter?

*nods* exactly. No more that +.5 or -.5 are odd or even.

*nods* exactly. No more that +.5 or -.5 are odd or even.
But +0.5 and -0.5 are a part of Q, isn't the issue whether or not odd/even applies to Z?

If odd/even only applies to N does that mean that -2 is neither odd nor even? or any negative number for that matter?
*nods* exactly. No more that +.5 or -.5 are odd or even.

*sighs* Someone has really screwed you up. Negative integers are odd and even in the same way positive integers are, i.e. depending on whether they are divisible by two.

Zero is even.

1. When you add an even (6) to an even (8) you get an even (14)
eg) 6+8=14

2. When you an odd (9) to an odd (3) you get an even (12)
eg) 9+3=12

3. When you add an odd (5) to an even (2) you get an odd (7)
eg) 5+2=7

If you try any of these examples with zero, you will see that it is even:

1. eg) even (4) + even (0) = 4 (even)

2. Cannot do this one becuase it invovles two odds and zero is even (try it and you'll see)

3. eg) odd (3) + even (0) = odd (3)

Therefore, zero is even.

http://mathworld.wolfram.com/NaturalNumber.html
This certainly doesn'help solve anything. ;)

But +0.5 and -0.5 are a part of Q, isn't the issue whether or not odd/even applies to Z?


En bref: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Fibonacci.html


Check liber quadratorum.

PS. Any post-euclidean textbook on geometry will proof this point as well.
Odd and Even are GEOMETRIC propositions after all.

You know, the set of even integers is usually expressed as 2Z for a reason... because if you take Z and multiply every member by 2, you have all the even integers which includes zero. The set of odd integers is written 2Z+1 for similar reasons.

http://mathworld.wolfram.com/NaturalNumber.html
This certainly doesn'help solve anything. ;)

Try here: http://mathworld.wolfram.com/EvenNumber.html

I think numbers are a social construct. They don't really exist except as part of mathematics, something made by humans.

*sighs* Someone has really screwed you up. Negative integers are odd and even in the same way positive integers are, i.e. depending on whether they are divisible by two.

If so... tmust have been my 12 or so years of work on the possibility of spaces defined with 'broken' dimensions.
( BTW: I think it is theoretically possible)

If so... tmust have been my 12 or so years of work on the possibility of spaces defined with 'broken' dimensions.
( BTW: I think it is theoretically possible)

12 or so years and you've only gotten to "thinking" so?

Still waiting on that citation.

*files note to ask his PhD math teacher tomorrow*

12 or so years and you've only gotten to "thinking" so?

Still waiting on that citation.

Thus when I wish to find two square numbers whose addition produces a square number, I take any odd square number as one of the two square numbers and I find the other square number by the addition of all the odd numbers from unity up to but excluding the odd square number. For example, I take 9 as one of the two squares mentioned; the remaining square will be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, a square number, which when added to 9 gives 25, a square number.

Yup. The problem is the translation of the basic axioma's of geometry from N into R - dimensional space. If the thing cannot be done... than that space would be meaningless.

It's BOTH

Wait, I know the answer! And it will solve this once and for all, as its irrefutable!

here we go:

IT DOESNT MATTER!

XD

It's EVEN, you idiots! GAH!!! :headbang:

Thus when I wish to find two square numbers whose addition produces a square number, I take any odd square number as one of the two square numbers and I find the other square number by the addition of all the odd numbers from unity up to but excluding the odd square number. For example, I take 9 as one of the two squares mentioned; the remaining square will be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, a square number, which when added to 9 gives 25, a square number.

Yup. The problem is the translation of the basic axioma's of geometry from N into R - dimensional space. If the thing cannot be done... than that space would be meaningless.

Yes... As I noted above from time to time the context requires a limitation to N. But in general every mathematician in the world knows that the even integers include zero.

Do you not know the simple algebra of rings? 2Z={..., -2, 0, 2, ...} is defined as the ring of "even integers." (Note that 2Z+1={..., -1, 1, 3, ...} is NOT a ring.)

Mathematicians have managed to define a continuous "factorial" function on R, yet you are still unable to deal with even and odd integers?! Seriously, I hope you didn't pay much more than postage for your degree.

Yes... As I noted above from time to time the context requires a limitation to N. But in general every mathematician in the world knows that the even integers include zero.




That is an extension of theory as bloody pointless ( AND invalid ) as the Blackett-derivation!

That is an extension of theory as bloody pointless ( AND invalid ) as the Blackett-derivation!

Why pointless? Why invalid? And why does every mathematician I can find disagree with you?

By the way... that citation?

How about a very nice application of integer parity... from Cornell? http://www.math.cornell.edu/~rperez/Putnam/parity.pdf

Why pointless? Why invalid? And why does every mathematician I can find disagree with you?

By the way... that citation?

Thus when I wish to find two square numbers whose addition produces a square number, I take any odd square number as one of the two square numbers and I find the other square number by the addition of all the odd numbers from unity up to but excluding the odd square number. For example, I take 9 as one of the two squares mentioned; the remaining square will be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, a square number, which when added to 9 gives 25, a square number.


There you go. Straight Fibonacci.


Pointless, and invalid, because you are straying beyond the limits were odd and even apply.

Pointless, and invalid, because you are straying beyond the limits were odd and even apply.

You are missing the point. In your example, you are intentionally restricted to a definition on N. In other cases, Z may be very meaningful and useful, and it is nice to have a definition for even and odd integers on Z.

Applications in abstract algebra abound.

Citation?

Seriously, I would love to be proven wrong and end this pointless debate. All I want is one. Edition, page number. That's it.

You prove yourself wrong:


Thus when I wish to find two square numbers whose addition produces a square number, I take any odd square number as one of the two square numbers and I find the other square number by the addition of all the odd numbers from unity up to but excluding the odd square number. For example, I take 9 as one of the two squares mentioned; the remaining square will be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, a square number, which when added to 9 gives 25, a square number.


If odd numbers less than one were not defined, why would you not simply add "all the odd numbers less than nine"?

HA! Mathematicians don't make qualifications unless there is something to qualify. Your own example openly declares that there are odd numbers less than one... because it goes out of its way to exclude them!

Citation?

Seriously, I would love to be proven wrong and end this pointless debate. All I want is one. Edition, page number. That's it.

Liber Quadratorum, 1225.

If you want to talk numbers, you ought to have a copy of it under your pillow.

Liber Quadratorum, 1225.

If you want to talk numbers, you ought to have a copy of it under your pillow.

Hmmm... Modern algebra wasn't even invented yet.

How about something from this century?


EDIT: And you still haven't given me a page number. :(

much adieu about nothing

You prove yourself wrong:

If odd numbers less than one were not defined, why would you not simply add "all the odd numbers less than nine"?

HA! Mathematicians don't make qualifications unless there is something to qualify. Your own example openly declares that there are odd numbers less than one... because it goes out of its way to exclude them!


Let's try it...

Sigma -1^2 + -3^2 + -5^2 ....you suppose you would reach infinity?
There are no odd numbers below 1. And there are no even numbers below 2.

What happens here is that Fibonacci simply and sensibly confines numerology to N, and not to INT. INT has no place whatsoever within numerology.

Let's try it...

Sigma -1^2 + -3^2 + -5^2 ....you suppose you would reach infinity?
There are no odd numbers below 1. And there are no even numbers below 2.

What happens here is that Fibonacci simply and sensibly confines numerology to N, and not to INT. INT has no place whatsoever within numerology.

Hey, if you want to do numerology -- the study of the occult significance of numbers -- you do that. And define odd and even however you want.

For the rest of the world, interested in real mathematics... well, I'm sure we'll get along whether you believe our well-established definitions or not.

Mathematics is, alas, so much bigger than Fibbonacci.

EDIT: And for the last time, it's Z, not "INT".

0 is EVEN. It says so in the bible.

Even is just a shorthand label meaning whatever set of numbers you want it to. The debate shouldn't be 'is 0 an even number:' it should be 'is 0 used as an even number more or less often than not.'

Regardless, I don't know much about math so I am looking to you to help me. I'm still in school learning how to mathematicize. For reference, my experience is limited to a small bit of programming and math up to vector and multivariable calculus.

number theory ( i.e. what I refer to as numerology)

Number theory is the study of the properties of the natural numbers N.
It includes such topics as prime numbers, including the prime number theorem, quadratic reciprocity, quadratic forms, diophantine approximation and diophantine equations, algebraic number fields, Fermat's last theorem and the methods developed to prove it.

http://www-groups.dcs.st-and.ac.uk/~history/Glossary/diophantine_approximation.html

Frankly... I don't give a darn for Z. It is you who cannot distinguish between N and other sets, not me.

As an added after-thought... most of today's serious physics assumes BTW that even N-space is too broad a definition of space. It is assumed ( by its practitioners ) that space should be solely confined to Even-numbered dimensional systems. I don't buy it... and will merrily continue to delve into the realm of N-space geometry. Which may lead to a break-up between physics and geometry... but frankly, I don't give a damn. The less engineering types that hang around in our halls, the merrier I will be.

Frankly... I don't give a darn for Z. It is you who cannot distinguish between N and other sets, not me.

Therein lies the problem. Also, I'm surprised at your lack of proficiency with English. Is it your second language?

Number theory is the study of the properties of the natural numbers N.

No. The special branch of Combinatorial Number Theory involves only the natural numbers N. Algebraic Number Theory extends the concept of numbers to include the members of some ring. There are a variety of other branches. The point is, you can't restrict the field to your narrow branch, and then claim that any definition that is "useless" in yours is invalid.

0 is indeed not a natural number, and is no more odd or even than (Root 3)/2.

0 is indeed not a natural number, and is no more odd or even than (Root 3)/2.

Another person who has never heard the phrase "even integer" or "odd integer", eh?

What are they teaching you kids?

I'm quite sure it is not considered either odd or even.

What are they teaching you kids?

3 + 5 = chair.

Neither. There is no zero. It is all a big conspiracy. The number that is actually there is huwnhfcsiwyucfrnwkuygjbhweuyjnesjrgntcsejkcrynsehercnsrcgu ({|}).

I'm quite sure it is not considered either odd or even.

Then I'll ask you for what the others have failed to provide: ANY reputable documentation from, say, the last century. A good web site will do... We have already seen at least two that label zero "even."

Neither; because dividing it by both an odd and an even number will still get you 0

So?

If you divide another number by 0 (ex 456/0) it will equal 1. there is only one exception to this. (I hope I am remembering all of this correctly) So zero apparantley does something. It is not the absence of value, or the absence of a number, it a number representing, simply, nothing. How many smileys do I have in this message? Even though there are not any, we still have to have a number to represent the value of none. That number is 0. Oh, and I have always been taught it is even.

Then I'll ask you for what the others have failed to provide: ANY reputable documentation from, say, the last century. A good web site will do... We have already seen at least two that label zero "even."

You could find at least a hundred websites stating that Dubya is a swell guy.
Doesn't alter the fact that he isn't.

However... if you wish for the opinion of a somewhat more important source than a website, I happily refer you to Dr. Taylor. Last noticed him expounding the limitations of odd and even at British Mathematical Colloquium in Edinburgh.

You could find at least a hundred websites stating that Dubya is a swell guy.
Doesn't alter the fact that he isn't.
leave the boss out of this

Another person who has never heard the phrase "even integer" or "odd integer", eh?

What are they teaching you kids?


Oh, we've all heard it a thousand times. We've also heard the phrase 'creationism' at least a thousand times. Still doesn't give it any weight worth mentioning. Until YOU get accredition from, for argument sakes, the Max Planck Institute or CERN, I suggest you limit yourself to programming.

Don't bother mentioning any US accredition. After Pons and Fleischman, no one takes THAT seriously.

So?

If you divide another number by 0 (ex 456/0) it will equal 1. there is only one exception to this. (I hope I am remembering all of this correctly) So zero apparantley does something. It is not the absence of value, or the absence of a number, it a number representing, simply, nothing. How many smileys do I have in this message? Even though there are not any, we still have to have a number to represent the value of none. That number is 0. Oh, and I have always been taught it is even.


Home taught or US taught?

I still say that zero is a decidedly odd number, of the queerest kind.

Zero is the origin. Basically on a measuring scale, you can take any variable and make it the origin. Say you want to make calculations on the scale of the speed of light. You can take that extremely large number and make it the origin. In effect the speed of light becomes zero, one light year or increment of that huge number become 1, 2, 3 etc. This way you can ease the burden of calculations which are usually cumbersome.

db

0 is nothing. It cannot be odd, or even.

this is like asking if 1 is a prime number :D :fluffle: :confused: :rolleyes: :confused: :confused: :confused: :confused: :confused:

Originally Posted by Branin
So?

If you divide another number by 0 (ex 456/0) it will equal 1. there is only one exception to this. (I hope I am remembering all of this correctly) So zero apparantley does something. It is not the absence of value, or the absence of a number, it a number representing, simply, nothing. How many smileys do I have in this message? Even though there are not any, we still have to have a number to represent the value of none. That number is 0. Oh, and I have always been taught it is even.

actually, numbers cannot be divided by zero, there would be no solution to any number(n) divided by 0
n/0=No solution

0 is not..... That's the fundamental principle. Worrying about it being odd or even means you don't even know what it is. Or rather, that you do not know that is it not.

0 is not directly classifiable....

It is also said that any number divided by itself equals 1:
1/1 = 1
2/2 = 1
-1/-1 = 1
-3/-3 = 1

However, what does 0/0=? If it does not = 1, then it is not a number, and therefore cannot be considered an even "number" nor an odd "number"....

0 is not.... simple as that; 0 is not even, 0 is not odd, 0 is not anything, 0 is simply not....

this is like asking if 1 is a prime number :D :fluffle: :confused: :rolleyes: :confused: :confused: :confused: :confused: :confused:

No. 1 is not a prime number. I tried to eat it with my number muncher, and I lost a life. Then I was eaten by a troggle. :(

No. 1 is not a prime number. I tried to eat it with my number muncher, and I lost a life. Then I was eaten by a troggle. :(
number muncher?

number muncher?

Yeah. You ever play that game as a kid?

Does anyone know what I'm talking about? Number Muncher? You controlled the little guy and you munched on prime numbers or multiples of 4 or whatever. And you got chased by troggles. Remember?

ooh, number muncher...i love that game...

the mean troggles always cornered me, though, so i lost a lot...wow, good memories

and i no that 1 isn't a prime number, but i just couldn't remember what it was called, and i wanted to see if any1 knew

Zero fits an interesting place in mathematics. It is not a true (natural) number. It represents the idea of nothing. Therefore it can not be odd, even, negative or positive.

Plus, I can tell you that it's not even:

Any even number, when divided by 2, will yeild an even number.

0 / 2 is 0. Keep doing this infinately (sp sorry tired) and you will never arive at anything other than zero. Therefore, it can't be an even number.

Sorry if that logic doesn't appeal to you. I can always just say it's an arbitraty part of mathematics. :p

Any even number, when divided by 2, will yeild an even number.


2/2 = 1

That was a typo I guess. And that's where the problem lies: Should it correctly be "natural", or "whole"?

Whoever said the division of an even number by two must yield a natural number? I thought it just had to be a whole number, negative, positive or 0.
By the 'natural' definition, no negative number is even, and I find that tricky to believe.

Yeah. You ever play that game as a kid?

Does anyone know what I'm talking about? Number Muncher? You controlled the little guy and you munched on prime numbers or multiples of 4 or whatever. And you got chased by troggles. Remember?
you got a link?

you got a link?

To a game I haven't played in 10 years? No. If anyone else finds one, it might be worth a try. Just reminds me of my childhood is all.

dude! it didn't even know i remembered that game. that's insane. oh, and my answer to the poll was wtf man. i hate math and think that anyone other than like say, a mathematiian or an engineer or phycisist or some math person is even thinking about this is eriously screwed up.

public boolean isEven (int n)
{
if (n % 2 == 0)
return true;
else return false;
}

isEven(0) returns true.
MMMMmmmMMM java

I wouldn't really label zero as being either odd or even, but if I had to, I would say it is even based on the fact that it lies between two odd numbers. If we're only looking at whole numbers. Dodgy mathematics perhaps...

Surely, attempting to justify it as being even by stating that 0 + odd = odd and 0 + even = even is flawed. As you are merely saying that odd = odd and even = even, the presence of the zero does nothing in such equations, therefore you're not proving anything, merely stating the definition of even.

Heh.

To me, it seems pretty clear that 0 is even...

An odd number can be expressed as 2K+1, where K is an integer.
An even number can be expressed as 2K, where K is an integer.

0 can be expressed as 2*0, and cannot be expressed as 2K+1.

Or, alternate definition - when converted into binary, an even number will end with a 0 while an odd number will end with a 1. By this definition, 0 is clearly even.

Also: we know that calling 0 odd will result in contradictions. An odd number plus an odd number must be even; however, 0 + 1 = 1.

Calling 0 even results in no contradictions.

And so on...

I can't believe this is a real discussion.. err.. argument. Whatever.

"An integer n is defined to be even if n = 2k for some integer k. ...we define an integer n to be odd if n = 2k+1 for some integer k."

--excerpt from "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang

There. In terms of integers. By published authors, in a published textbook, for an actual college mathematics course. If you want to debate this, you're going to have to bring a better citation to the table.

We find the dumbest things to argue about don't we? What happened to peace and harmony.


MY 200th POST! :) :D

You could find at least a hundred websites stating that Dubya is a swell guy.
Doesn't alter the fact that he isn't.

However... if you wish for the opinion of a somewhat more important source than a website, I happily refer you to Dr. Taylor. Last noticed him expounding the limitations of odd and even at British Mathematical Colloquium in Edinburgh.

Now now... You know we all need something we can look up. Is this really so difficult?

Oh, we've all heard it a thousand times. We've also heard the phrase 'creationism' at least a thousand times. Still doesn't give it any weight worth mentioning. Until YOU get accredition from, for argument sakes, the Max Planck Institute or CERN, I suggest you limit yourself to programming.

Who said I know anything about programming?

By the way, from where is your accreditation? Seriously, just curious.

Still waiting on that citation.

I still say that zero is a decidedly odd number, of the queerest kind.

Okay, that's even more screwed up than calling it neither odd nor even!! On what grounds can you possibly call it odd?! It satisfies literally every possible definition of an even number except when you restrict yourself to the natural numbers... and even then it depends on to whom you are talking, since for so much of mathematical history it has been considered a "toss-up" whether to call zero a member of N. It really comes down to convention.

At any rate, once you are in Z, the evens are defined as ALL numbers that can be written n=2k, or numbers that can be divided by 2 with no remainder. I cannot believe we are having a conversation in which anyone seriously disputes this!

So what is 0 / 0 ?

Is it 0 because 0 / x = 0 ?

Is it undefined because x / 0 is undefined?

Or is it 1, because x / x = 1?

I can't believe this is a real discussion.. err.. argument. Whatever.

"An integer n is defined to be even if n = 2k for some integer k. ...we define an integer n to be odd if n = 2k+1 for some integer k."

--excerpt from "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang

There. In terms of integers. By published authors, in a published textbook, for an actual college mathematics course. If you want to debate this, you're going to have to bring a better citation to the table.

Thank you!! I would have done this myself, but my math books are at least an hour and a half away--and me with no car. So, any takers?

Indeed, what are they teaching kids these days?

0 is an integer. It's even, just like any other number that can be expressed in the form 2k, where k is an integer. Including negative numbers.

Only integers get to be even or odd, and they all get to play the game.

n/0 is undefined in finite mathematics, and infinitely large (small) if you care about the concept of infinity. As long as n <> 0.

0/0 = 17 (17*0 = 0). Or whatever other number you like. The technical term is indeterminate.

If you want to discuss other rings, fields, groups, or algebras, the rules may be different. But when you're talking integers, it's quite clear.

Okay, that's even more screwed up than calling it neither odd nor even!! On what grounds can you possibly call it odd?! It satisfies literally every possible definition of an even number except when you restrict yourself to the natural numbers... and even then it depends on to whom you are talking, since for so much of mathematical history it has been considered a "toss-up" whether to call zero a member of N. It really comes down to convention.

At any rate, once you are in Z, the evens are defined as ALL numbers that can be written n=2k, or numbers that can be divided by 2 with no remainder. I cannot believe we are having a conversation in which anyone seriously disputes this!
I think he means odd as in unusual.

I think he means odd as in unusual.

Well, it is that.

It is even.

/////
Definition: An even number is one that can be divided into two and remain an integer.

Postulate: an even number plus an odd is an odd number.
0+3=3; 3/2=1.5 is not an integer; therefore, 0+{odd number1}={oddnumber2}

Postulate: an even number plus an even number is even
0+2=2; 2/2=1 is an integer; therefore, 0+{even number1}={even number2}

Postulate: an even number plus 1 is an odd number and an odd number is equal to an even number.
0+1=1; 1/2=.5 is not an integer therefore it is odd; 0+2=2; 2/2=1 is an integer therefore it is even.

Identity property n=n, which can demonstrate the property that n is in the same realm as itself.
Any number times 2 is equal to an even number.
0*2=0
/////

Postulates are generally accepted truths, and therefore 0 is a generally accepted even integer. Earlier posts have also mentioned other definitions and laws that further prove the statement 0==even

An earlier post claims that zero is a word and not a number. This is not true as 0 can be used in mathematical operations, it can be equal to a mathematical expression, and has many other traits that classify it as a real rational number.

So what is 0 / 0 ?

Is it 0 because 0 / x = 0 ?

Is it undefined because x / 0 is undefined?

Or is it 1, because x / x = 1?

I like the way you think. Very interesting example.

So what is 0 / 0 ?

Is it 0 because 0 / x = 0 ?

Is it undefined because x / 0 is undefined?

Or is it 1, because x / x = 1?

Even though it is classified as "undefined" x/0 is infinity...

this can be seen in the operation of the normal divisor....

Ok,

1/10 = .1
1/9 = .111~
1/8 = .125
1/7 = .143~
1/6 = .167~
1/5 = .2
1/4 = .25
1/3 = .333~
1/2 = .5
1/1 = 1
1/(.9) = 1.111~
1/(.8) = 1.25
1/(.7) = 1.429~
sic... in the given equation 1/x = y

as x approaches 0, y approaches infinity

If x is 0, y is infinite (aka undefined).

0/0 becomes even more complicated..... if nothing, is divided by nothing, then you can assume nothing would remain; however, how would you divide nothing in the first place, even by itself..... therefore it would still be undefined. Under the concept of 0/x we can assume it is 0 by the normal rule, though under x/0 we can assume it is undefined.... Of course, all this operates under the assumption that 0 "acts" like a number... but, in all truth, 0 is not a number, it is the absense of a number.... so is it right, under any rule, to treat it as such; and if so, what is the justification to do so?

(semantic slight sarcasm)
zero = 0 = nothing
if nothing is even
than 2 and its factors can not be even, unless they are nothing
but then they would cease to exist
if nothing is odd
then every other number in existance is nothing
and math is cut in half

but if nothing is neither odd nor even then you dont have to think aout any of that

but thats all just semantics

(reality of opinion)
0 is even
you can have two halves of nothing

(overthought misinformation)
but back to overthought, all numbers are even
even numbers can be divided by 2
one fractions and decimils are introduced, odd becomes irrelevant
because now everything can be split into two equal halves
no matter how small or precise they may be

Here is something for you to think about...

1 / 3 is 0.333333333333333333 with 3's continuing on forever...

3 * 1 / 3 = 1 obviously

but 3 * 0.33333333333333333333 = 0.9999999999999999 with 9's continuing on forever

Even though it is classified as "undefined" x/0 is infinity...

No. It's not. The limit of a/x as x goes to 0 is undefined and "goes to infinity," but this is not nearly the same thing as to say that x/0=infinity.

Why? Because if this were true, then 1/0=infinity. But then 1=0*infinity, which is impossible.

(Another reason is that to do the limit, you have to know on which direction you are coming in to zero... if from the positive side, you go to positive infinity, if from the negative then to negative infinity--assuming the numerator is positive. So "at" zero one often enough has the situation that the "value" of the expression would be BOTH positive and negative infinity. Certainly no equality here!)

In advanced calculus, one may sometimes treat infinity as a number, in which case it is often acceptable to "fill in the hole" at zero denominators with the "number" infinity... but in general you have to be extremely careful about saying that sort of thing. It only works under certain special circumstances.

0/0 becomes even more complicated.....

Yes, but not at all in the way you describe it. 0/0 is, of course, undefined because it involves division by zero. It is, on the other hand, one of the instances in which the limit of an expression as the denominator goes to zero may exist. If both numerator and denominator go to zero, then you actually have to do the work to see if the zeros cancel each other out...

The limit may ultimately be undefined, or it may go to a real value. The point at 0, however, remains undefined.

Of course, all this operates under the assumption that 0 "acts" like a number... but, in all truth, 0 is not a number, it is the absense of a number.... so is it right, under any rule, to treat it as such; and if so, what is the justification to do so?

Zero is a number. It only "looks" like "the absence of a number" because most of the time we deal with only the natural numbers. It is a member of the ring of integers necessary to that ring's closure on addition.

4 + (-4) = 0. All numbers.

If you prefer to think that it is "really" not a number, fine--that's philosophy, not mathematics.

Why are we still doing this?

Why are we still doing this?

Good question.

I blame society.

this is a fun part of math, lol.
which again proves that classes suck if teachers do.
we never got stuff like this just really annoying interpolarisation n stuff:(

but my answer would be even(just see the above posts theres no denying that imo)

zero is number that you can divided in all the numbers. as that you can say that he even ,divided by 3 , and such as.
but I don't think you really can say that he even, like you can't say the infinity is even.
I prefer to use that definitions only on entire numbers.

zero is number that you can divided in all the numbers. as that you can say that he even ,divided by 3 , and such as.

Yeah... so? The definition of an even number is that it can be divided by 2, NOT that it can be divided by two and nothing else!!

but I don't think you really can say that he even, like you can't say the infinity is even.
I prefer to use that definitions only on entire numbers.

Well, your thoughts and preferences are up to you. The rest of us are concerned with what real mathematicians think.

"Any number" mod 2 = 0, if and only if that number is even


Kindergarten method:
If you have an even number of blocks you can make two equally high towers from them. If you have zero blocks, you can make two towers with equaly height (zero).

"Any number" mod 2 = 0, if and only if that number is even


Kindergarten method:
If you have an even number of blocks you can make two equally high towers from them. If you have zero blocks, you can make two towers with equaly height (zero).


the answer is no.

if you have no bricks, you can make no towers.

Every poll should automatically include "wtf, man?" as an option.

isEven(0) returns true.

just because java thinks it is even, doesn't make it even.

the answer is no.

if you have no bricks, you can make no towers.
No tower is a tower with height zero.

Think of the WTC: everyone knows it's there, but you can't see it

Neither. In order for a number to be odd or even it must actually be a number, and since the symbol 0 represents the *absence* of a number it can't be either odd or even. That's also why a number divided by zero equals that number, it's just a fancy way to say that the number in question isn't being divided.
0 is too a number. It's the number of boats I own. Those little boxes from second grade represent the absence of a number :)

Zero is neither odd nor even. It is the origin of all numbers, the base from which they all come. It is neutral.

0 = nothing, the absense of anything or everything...

If you have no blocks, you can build no towers; and so have no towers.

The argumentative tactic, used to imply that you have a tower of height 0; is called "sophistry".... The use of a plausible argument "0 blocks is a number of blocks" used to back a fallacious conclusion "so therefore I can build a tower of 0 height from 0 blocks", under the guise of a logical argument.

However, logically, your argument fails, because without the blocks, you cannot "build" so you are honestly not doing anything.

A "0" height tower is not a tower that was not ever built, by no one with nothing. It's a figment you have created, based on faulty reasoning, which logic punches through like a hot knife through butter.

0 is a number, and it is even.

The only people who are arguing against this are people with no qualifications in mathematics. Mathematicians are in uniform agreement that 0 is a number (integer), and it is even. That means this entire debate is rather like watching a man with no arms and only one leg assault a modern, entrenched infantry division. Funny, but ultimately tragic.

0 = nothing, the absense of anything or everything...

If you have no blocks, you can build no towers; and so have no towers.

The argumentative tactic, used to imply that you have a tower of height 0; is called "sophistry".... The use of a plausible argument "0 blocks is a number of blocks" used to back a fallacious conclusion "so therefore I can build a tower of 0 height from 0 blocks", under the guise of a logical argument.

However, logically, your argument fails, because without the blocks, you cannot "build" so you are honestly not doing anything.

A "0" height tower is not a tower that was not ever built, by no one with nothing. It's a figment you have created, based on faulty reasoning, which logic punches through like a hot knife through butter.
As I stated the first time:

That is the "kindergarten tactic". So even people who don't know ANYTHING about math will get it.


Anyway... Your argument for zero to be a number or not: It's not proven. One side says it is, the other says it isn't. There is no definition.

As I stated the first time:

That is the "kindergarten tactic". So even people who don't know ANYTHING about math will get it.


Anyway... Your argument for zero to be a number or not: It's not proven. One side says it is, the other says it isn't. There is no definition.

Except the "Kindergarden tactic" as you put it, is sophist in design. It's a fallacious argument, designed to look plausible; but when analyzed logically, it fails.

it's odd, even, odd, even etc.
so:

3 is odd, so 2 and 4 must be even;
1 is odd, so 0 and 2 must be even.

can't believe not everybody knows that

Except the "Kindergarden tactic" as you put it, is sophist in design. It's a fallacious argument, designed to look plausible; but when analyzed logically, it fails.
Yes... that's what I said... kindergarten. I know it's faulty logic reasoning, but it works for those who never had to do much with either math or logic reasoning

Zero is neither odd nor even. It is the origin of all numbers, the base from which they all come. It is neutral.

No, nothing "comes" from zero. Multiply it by anything and you get zero. Add it to anything, and you only get what you started with.

While zero is the "origin" from which we measure positive and negative magnitude, the generator of the integers is one. You can reach ANY integer by starting with one, and then adding or subtracting one. The integers are a cyclic group with generator 1, and a ring once you add multiplication to the mix. :D

0 = nothing, the absense of anything or everything...

If you have no blocks, you can build no towers; and so have no towers.

The argumentative tactic, used to imply that you have a tower of height 0; is called "sophistry".... The use of a plausible argument "0 blocks is a number of blocks" used to back a fallacious conclusion "so therefore I can build a tower of 0 height from 0 blocks", under the guise of a logical argument.

However, logically, your argument fails, because without the blocks, you cannot "build" so you are honestly not doing anything.

A "0" height tower is not a tower that was not ever built, by no one with nothing. It's a figment you have created, based on faulty reasoning, which logic punches through like a hot knife through butter.

By your argument, negative numbers do not exist either. And in the context of the philosophy of mathematics, there may be some sense to this--and even some important insights.

But you have to realize that there are other considerations besides what numbers seem "natural." First, mathematics is instrumental as well, and its definitions refer to things that are useful, like negative numbers and zero. Also, there are certain properties of a set that seem to have both instrumental and philosophical implications... Such as completeness.

The point is, ultimately we come up with the definitions for a variety of reasons somewhat remote from building blocks and fingers. And we--by which I mean the entire mathematical community of the last few hundred years--agree that it makes sense to call zero an even number.

As I have pointed out before, it is a member of the ring of even integers generated by 2: Start with two, and then add or subract whatever multiples of two you want. What you end up with is the set {...,-2,0,2,...}, which has the very nice properties that if you add any two members of the set, the sum is in the set, and if you multiply any two members the product is also a member of the set. (Not true of the odd numbers, of course.)

By your argument, negative numbers do not exist either. And in the context of the philosophy of mathematics, there may be some sense to this--and even some important insights.

But you have to realize that there are other considerations besides what numbers seem "natural." First, mathematics is instrumental as well, and its definitions refer to things that are useful, like negative numbers and zero. Also, there are certain properties of a set that seem to have both instrumental and philosophical implications... Such as completeness.

The point is, ultimately we come up with the definitions for a variety of reasons somewhat remote from building blocks and fingers. And we--by which I mean the entire mathematical community of the last few hundred years--agree that it makes sense to call zero an even number.

As I have pointed out before, it is a member of the ring of even integers generated by 2: Start with two, and then add or subract whatever multiples of two you want. What you end up with is the set {...,-2,0,2,...}, which has the very nice property of being closed on both multiplication and addition (the sum of any two even numbers is even, and the product of any two even numbers is even).

Circular definition, defining a thing by itself. Therefore another sophistry.

0 represents nothing, it is not... It's the lack of anything. As well, negative numbers do not exist. They are all constructs, because humans, and even mathmaticians, refuse to look at reality; and therefore, to prevent themselves from actively looking at reality (and dealing with it), they develope relative abstracts such as "0" and negative numbers (neither of which exist) to deal with things they themselves refuse to.

In Physics, you cannot have negative dimensions. However, you CAN have negative vectors. 0 indicates no movement. It is neutral; neither positive or negative. Just clearing that up. So while you can't constrcut a space of area -1^3, you can move backwards. Subtraction is just addition of a negative number.

Zero is even. It fits the sequence (even, odd, even, odd, even, odd). At NO POINT is this integer-pattern broken. It is nonsense to belive there are 3 odd integers in a row.

The mathematics behind each case exist, JAVA coders believe it, it's foolish not to believe it. The only time people decide "it's not even or odd" when they confuse it with "it's not positive or negative"

if(n.value % 2 = 0){
n.type = even;
}

Circular definition, defining a thing by itself. Therefore another sophistry.

0 represents nothing, it is not... It's the lack of anything. As well, negative numbers do not exist. They are all constructs, because humans, and even mathmaticians, refuse to look at reality; and therefore, to prevent themselves from actively looking at reality (and dealing with it), they develope relative abstracts such as "0" and negative numbers (neither of which exist) to deal with things they themselves refuse to.
How do you explain moving backwards? Or taking a cube away from the big cube?

In Physics, you cannot have negative dimensions. However, you CAN have negative vectors. 0 indicates no movement. It is neutral; neither positive or negative. Just clearing that up. So while you can't constrcut a space of area -1^3, you can move backwards. Subtraction is just addition of a negative number.

Zero is even. It fits the sequence (even, odd, even, odd, even, odd). At NO POINT is this integer-pattern broken. It is nonsense to belive there are 3 odd integers in a row.

The mathematics behind each case exist, JAVA coders believe it, it's foolish not to believe it. The only time people decide "it's not even or odd" when they confuse it with "it's not positive or negative"

if(n.value % 2 = 0){
n.type = even;
}

Irrelevant, "-" vectors only exist in abstract relation to the viewer.

How do you explain moving backwards? Or taking a cube away from the big cube?

You don't "move backwards" you move... "backwards" doesn't exist, it's an abstraction.

Tekania: why do you believe in the old Roman Numbersystem?

Irrelevant, "-" vectors only exist in abstract relation to the viewer.

Hell, "+" vectors only exist in abstract relation to the viewer!

What "makes" a vector other than its relation to arbitrary reference points? Even if you try to get down to the most basic material sense of distance in space, you ultimately have to deal with the fact that the basic notion of '"this way" and "that way" are abstractions. There is no way to point to anything without the abstraction "That."

You don't think "that" is an abstract concept? Consider that at one time you say, "that" pointing to one thing, while at another time "that" applies to something else.

For someone who seems so interested in philosophy, I'm surprised you don't remember those first few chapters in Hegel's Phenomenology.

You don't "move backwards" you move... "backwards" doesn't exist, it's an abstraction.

Then what is "forwards"?

Tekania: why do you believe in the old Roman Numbersystem?

Who said I believed in the old Roman Numeral System? And how can you "believe" in a number system?

It's considered even by all mathematicians... what else do you want?

Then what is "forwards"?

There is no forwards.... it's another abstraction.

There is no forwards.... it's another abstraction.

Hilarious.

So we've gone from "zero is neither even nor odd, because only positive numbers exist," to now "nothing about the concept of 'number' is real."

Which entirely evades the point, because whether integers are "real" or not, we define them to be either odd or even; and zero is even.

Hilarious.

So we've gone from "zero is neither even nor odd, because only positive numbers exist," to now "nothing about the concept of 'number' is real."

Which entirely evades the point, because whether integers are "real" or not, we define them to be either odd or even; and zero is even.

BAC

Exactly. Number parity is just a concept, which has a definition.

0 is even under just about every practical, theoretical or formal definition.

BAC

Is that supposed to mean something?

Just because it is an abstraction, doesn't mean it doesn't exist. It does exist: AS AN ABSTRACTION!

Just because it is an abstraction, doesn't mean it doesn't exist. It does exist: AS AN ABSTRACTION!
Can I exist as an abstraction too?

Can I exist as an abstraction too?
On this forum you can

On this forum you can
YAY … And my old trig teacher said I could be obtuse too! This is so cool

YAY … And my old trig teacher said I could be obtuse too! This is so cool
obtuse?

obtuse?
As in > 90 degree angle


Also kind of slang for "dumb"

even numbers have a difference of 2

so it would go -2 0 2 4 6...

Christ, people. Zero is a fairly mundane, even number. If you want a -really- complex discussion, debate the number i.

WTF, man?

has any one yet provided a reputable web site which will prove wether 0 is even or not

No, but I cited my Math 311 textbook, which is worth more than a website.

No, but I cited my Math 311 textbook, which is worth more than a website.
What is the math course titled?

There is a simple arguement for proving 0 is even. Even numbes are always 1 away from an odd number and 2 away from an even number. 0 is 1 away from both 1 and -1. Ergo 0 is even.

1) You don't have to prove anything. Zero is even by the definition of 'even'. I don't think this can be made simpler.

2) Kanteletar: the course is titled 'Set Theory'. The exact quote and citation is in a previous post in this thread.

n/0=UNDEFINED, therefore I conclude that 0 is neither. Also, it is not an integer, but it is a natural number.

Christ, people. Zero is a fairly mundane, even number. If you want a -really- complex discussion, debate the number i.
Do you mean debate whether it is even or odd? Because i is imaginary, and it is definitely not even or odd.

I would have to say 0 isnt even or odd. 0 is just like saying nothing, if I said i had 0 keyboards, it is inferring I have none. I think it is just used as a filler between and at the end of long numbers and to imply none. I dont have any idea what I'm talking about. :confused:

-5:odd
-4:even
-3:odd
-2:even
-1:odd
0: ???
+1:odd
+2:even
+3:odd
+4:even
+5:odd

I'm going for even.

I give up. This thread is only proving that 105 out of 260 people (at the time of this writing) value their totally unqualified and proven wrong opinions over hard evidence and an overwhelming consensus of people in math professions.

If professionally-accepted documentation of the definition of the term "even" is not enough to convince you, you cannot be helped.

It's like pointing out a monkey to man and saying "that's a monkey," only to have him respond, "no, it's a cow." Then, when you provide a dictionary that defines the word "monkey," an encyclopedia with pictures and descriptions of monkeys, and a panel of monkey experts who all conclude that it's indeed a monkey, the man continues to say, "nah, I still believe it's a cow."

So, believe what you want. It's painfully obvious that you have no idea what you're talking about.

:P Hey, I'm doing the whole Math degree thing...
But then, you're not really talking to me because I would intuitively accept that zero is even.

But just to point out, that perhaps some other's on here are just as qualified as you to speak about it.

Besides, just because professionals accept it, that's no reason not to question it. How else does mathematics develop if we don't question the logic?

Also, 1 satisfies the definition of prime, yet we don't technically consider it a prime. I would say that when it comes to the definition of even, zero is a special case because it doesn't really satisfy the definition given by many on here. That is to say that, the definition being:

x + Even = Even
x + Odd = Odd

By replacing the x with zero, we're not really affecting the equation. Merely stating that some even number is itself or some odd number is itself. Zero doesn't do anything over addition.

But then I may just be being facetious...

I hate complex numbers, damn that man that decided negative numbers should have roots too.
but lets subsitute for x
3+4=7
4+4=8

3+3=6
4+3=7

hmm
x+even can= odd
x+odd can =even

but lets subsitute for x
3+4=7
4+4=8

3+3=6
4+3=7

hmm
x+even can= odd
x+odd can =even

*cough*

x + even = even = even + x
x + odd = odd = odd + x

I think you missed the point of my post entirely...

I'm not saying the definiton is wrong, I'm saying you can't use the definiton to prove that zero is either odd or even since it does nothing over addition.

By substituting zero you are merely stating that some odd number is odd or that some even number is even.
even+even=even
odd+even=odd

0+2=2
0+1=1

even+even=even
odd+even=odd

0+2=2
0+1=1

...dammit, too fast...

:P

It's not really a valid proof. I don't think atleast.

...dammit, too fast...

:P

It's not really a valid proof. I don't think atleast.
no your just to slow

no your just to slow

Ah, but I can spell surely that counters any 'slowness' that afflicts me.

What do you have?

Ah, but I can spell surely that counters any 'slowness' that afflicts me.

What do you have?
i dont know but your not graded on spelling in math class

Guys, this is not an opinion thing, this is a mathmatical proof.

ZERO IS NIETHER ODD NOR EVEN!

Zero is not a number, and therefor cannot be considered odd or even. It is the lack of a value whether it be positive or negitive. Zero IS NOT a number.

Zero IS NOT a number.

Zero is not a natural number.
Zero IS an integer, and a rational number, and a real number, and a complex number.

http://www.math.utah.edu/~alfeld/math/numbers.html

Guys, this is not an opinion thing, this is a mathmatical proof.

ZERO IS NIETHER ODD NOR EVEN!

Zero is not a number, and therefor cannot be considered odd or even. It is the lack of a value whether it be positive or negitive. Zero IS NOT a number.
Since zero is the reference point by which a number is positive or negative this (the part I bolded) is a rather trivial point.

Zero is not a natural number.
Zero IS an integer, and a rational number, and a real number, and a complex number.

http://www.math.utah.edu/~alfeld/math/numbers.html

I posted this link earlier in the thread.
http://mathworld.wolfram.com/NaturalNumber.html

is it a vowel or a consonant? (makes the same sense as the question)

Neither, as it holds no value to be be divided.

Zero is not a natural number.
Zero IS an integer, and a rational number, and a real number, and a complex number.

http://www.math.utah.edu/~alfeld/math/numbers.html
ok this is from some sort of educational facility, so now we have proof 0 is a number, yet we have yet to get a proof like this on odd or even or should i say now even or not odd or even

ok this is from some sort of educational facility, so now we have proof 0 is a number, yet we have yet to get a proof like this on odd or even or should i say now even or not odd or even


Back on page 8...
I can't believe this is a real discussion.. err.. argument. Whatever.

"An integer n is defined to be even if n = 2k for some integer k. ...we define an integer n to be odd if n = 2k+1 for some integer k."

--excerpt from "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang

There. In terms of integers. By published authors, in a published textbook, for an actual college mathematics course. If you want to debate this, you're going to have to bring a better citation to the table.

If you need an internet site


Zero, on the other hand, is very even. It can be written in the form 2*n,
where n is an integer. Odd numbers can be written in the form 2*n + 1.
Note that this lets you talk about whether negative numbers are even and odd.

http://mathforum.org/library/drmath/view/57062.html
Which you will see is the same as the excerpt from the textbook.

public boolean isEven (int n)
{
if (n % 2 == 0)
return true;
else return false;
}

isEven(0) returns true.

You don't need the else, because the first return will break out without it. Also, I think "== 0" is wasteful. (Note, is this C++ or Java? I am writing it in C++ format)

Try this:

public boolean (you mean bool?) isEven (int n)
{
if (!(n % 2))
return true;
return false;
}

according to the NYS Board of Regents, it is niether. Trust me on this. I paid for this mistake on the Math A Regents examination.

They could be wrong, but then i would have to be pissed at the State. And the government is never wrong so, zero is niether.

according to the NYS Board of Regents, it is niether. Trust me on this. I paid for this mistake on the Math A Regents examination.

They could be wrong, but then i would have to be pissed at the State. And the government is never wrong so, zero is niether.

What are regents?
What level of math?
Who marks them?

What are regents?
What level of math?
Who marks them?


not a new yorker?

New York State standardized tests in Math, Science, English, Foriegn Language and History.
One takes 2 maths, 2 histories, 1 language, 2 Sciences and 1 English, over the course of four years.

high-school 1 and 2 level math

teachers...and they cheat FOR the kids(off-topic(maybe later))

not a new yorker?

New York State standardized tests in Math, Science, English, Foriegn Language and History.
One takes 2 maths, 2 histories, 1 language, 2 Sciences and 1 English, over the course of four years.

high-school 1 and 2 level math

teachers...and they cheat FOR the kids(off-topic(maybe later))

Nope, I'm a New Zealander.

Ah, no offense but I've found that highschool is not always the best source of correct information in mathematical technicalities.
A highschool course is certainly not reputable enough to rebut the mathematical textbook reference given earlier.

You don't need the else, because the first return will break out without it. Also, I think "== 0" is wasteful. (Note, is this C++ or Java? I am writing it in C++ format)

Try this:

public boolean (you mean bool?) isEven (int n)
{
if (!(n % 2))
return true;
return false;
}

Or even shorter (the syntax may be off as I don't know C++ or Java):


public boolean isOdd (int n)
{
return (n % 2);
}

You don't need the else, because the first return will break out without it. Also, I think "== 0" is wasteful. (Note, is this C++ or Java? I am writing it in C++ format)

Try this:

public boolean (you mean bool?) isEven (int n)
{
if (!(n % 2))
return true;
return false;
}
if (x == 0) and if (!x) should produce identical code.

Here is something for you to think about...

1 / 3 is 0.333333333333333333 with 3's continuing on forever...

3 * 1 / 3 = 1 obviously

but 3 * 0.33333333333333333333 = 0.9999999999999999 with 9's continuing on forever

OMG, there was much debate about this in my high school pre-calc class.

_
.9 = 1, but nobody fricken believes it. It's amazing.

Here is something for you to think about...

1 / 3 is 0.333333333333333333 with 3's continuing on forever...

3 * 1 / 3 = 1 obviously

but 3 * 0.33333333333333333333 = 0.9999999999999999 with 9's continuing on forever


OMG, there was much debate about this in my high school pre-calc class.

_
.9 = 1, but nobody fricken believes it. It's amazing.

Oh you poor misguided persons. Didn't your teachers tell you that 1/3 is NOT
0.33333333333333333333333333r forever? 0.3333333r is just as close as you can get to 1/3 in decimal. It never actually gets to 1/3. Nobody believes that 0.9r is 1 because it ISN'T.

Oh you poor misguided persons. Didn't your teachers tell you that 1/3 is NOT
0.33333333333333333333333333r forever? 0.3333333r is just as close as you can get to 1/3 in decimal. It never actually gets to 1/3. Nobody believes that 0.9r is 1 because it ISN'T.
ahem...

it is

whats the relevancy of this topic?

n/0=UNDEFINED, therefore I conclude that 0 is neither.I don't think division by zero has any relevance in the odd/even debate.

Division of a number by an odd number does not guarantee odd-ness or even-ness (or even integerness, even if the first number is an integer to start with) and the same with division by an even one.

There's perhaps room to suggest that odd*0=undefined_odd_or_evenness(=0) because 0 is undefined to start with and hence zero has undefined odd_or_evenness, but as odd*odd=odd but all other multiples are even, because the zero might be the product of being even*0=0 zero must be even. It should (by that argument) be at least 75% even... (I leave it as an excercise by the reader to discover the flaw in that explanation... :))

Essentially I say zero is even, but there are many ways (like the above) to exclude zero from the sequence if you try hard enough. There are less contrived and more believable ones, but I was aiming for contrived on that occasion. There are even a few tricky ways to make it look odd, but you have to really push and I didn't quite manage to convince myself of the example I was going to give (though I was desperately trying to ignore the fact that it was complete bunk)...


Also, it is not an integer, but it is a natural number.Have you got that the wrong way round? It most definitely is an integer (Z, non-inclusively all numbers between -infinity and +infinity) but the main debate is whether it is in the natural/counting numbers (N, starts at either zero or one, depending on purpose and background of usage, ends just short of +infinity).


And, going back a bit in the thread, having two towers of zero height can be different from having no towers of any height... Or it can be the same. Though I don't know how a teacher would react between someone saying "I decided not to build any towers of bricks" and "I decided to build a tower of bricks of zero height." :)

Oh you poor misguided persons. Didn't your teachers tell you that 1/3 is NOT
0.33333333333333333333333333r forever? 0.3333333r is just as close as you can get to 1/3 in decimal. It never actually gets to 1/3. Nobody believes that 0.9r is 1 because it ISN'T.

Ahh, but you are the one who has been misguided.

If .9 repeating is not the same as 1, then why don't you name a number between them?

ahem...

it is

If it were, people would just write 1, and not 0.999999999r.

Oh you poor misguided persons. Didn't your teachers tell you that 1/3 is NOT
0.33333333333333333333333333r forever? 0.3333333r is just as close as you can get to 1/3 in decimal. It never actually gets to 1/3. Nobody believes that 0.9r is 1 because it ISN'T.
That is such a silly statement. It never gets to 1/3? It never gets anywhere. It is a number, it's value doesn't change. It is defined as equaling 1/3. It represents the exact same amount. If you only have 10, 1000, or 65465466542310232146546^98234098 digits it is not equal to 1/3, but the number we're talking about is expressed as an infinite number of 3s.

If it were, people would just write 1, and not 0.999999999r.
People do just write 1. The only time I've ever seen 0.99999r ever written is for the purpose of this silly argument.

According to the Rhode Island Math League, 0 is even.

According to the Rhode Island Math League, 0 is even.
can you give a link

can you give a link

Google is a good source - if you enter "is zero even", you get a large number of hits. Pick one, including mathforum.org or straightdope.com.

0 is even, unless you're playing roulette.

Google is a good source - if you enter "is zero even", you get a large number of hits. Pick one, including mathforum.org or straightdope.com.

0 is even, unless you're playing roulette.
yes becouse then its green

Hmmm, the simplest answer I can think of it even, but technically it would be neither. For it to be even you could times it by any other even number or an odd number and get an even number higher than itself, and zero is a real number, so negatives don't count with it, so I would assume that it is even being the short answer, and neither being a long answer...

Hmmm, the simplest answer I can think of it even, but technically it would be neither. For it to be even you could times it by any other even number or an odd number and get an even number higher than itself, and zero is a real number, so negatives don't count with it, so I would assume that it is even being the short answer, and neither being a long answer...

Why do you think "higher than itself" has anything to do with the definition? It's true that any positive even number multiplied by a positive number will give you a larger even number, but that's a consequence of even numbers, not a definition for them.

0 is even. Whether you go for the long or short definition, 0 is even.

Why do you think "higher than itself" has anything to do with the definition? It's true that any positive even number multiplied by a positive number will give you a larger even number, but that's a consequence of even numbers, not a definition for them.

0 is even. Whether you go for the long or short definition, 0 is even.

IF every natural number is either odd or even AND zero is a natural number, THEN zero is even.

For zero to be even, zero needs to be natural. This is where the problem lies...

IF every natural number is either odd or even AND zero is a natural number, THEN zero is even.

For zero to be even, zero needs to be natural. This is where the problem lies...

No, it really doesn't. Show me any mathematical source that says only natural numbers--and not integers--have parity. We already have several that say otherwise.

(I really wish I could stop answering these people... but it's so hard to let ignorance go without correction.)

i cant believe this thread is still going

even because 10 finishes by a zero. But 6,944,848,626,654,744,869 finishes by a 9 : it is an odd number.

i dont really understand what i am saying... :confused:

I always thought 0 was both (and neither in some strange way)...

At this point I see two possibilities. The people who say zero isn't even are either just trying to upset us math-heads, or sincerely (though inexplicably) uncomfortable with the WIDELY accepted mathematical definition of evenness.

Anyway, by official decree, those who refuse to accept the following are boneheads:

0. Zero is a number.
1. Zero is an even number.
2. Divisibility by zero has nothing to do with evenness.
3. You can have two towers of zero height. You can have eighty-nine trillion towers of zero height.
4. .3r = 3/9 = 1/3.
5. .9r = 9/9 = 1.
6. A dubious interpretation of a translated quote from an 800-year-old text, even if it was written by Fibonacci, does not trump every serious treatment of number theory since Russell and Whitehead.
7. The stubbornly ignorant should be sterilized.

Please post a contradiction so I can sit back and laugh at you.

Zero isn't a number. Zero is the symbol for the lack of a number, and the concept of even and odd in math only apply to numbers. But then again, I got a C on my last math test, so I don't know.

Odd numbers are non zero positive integers not divisible by two. Even numbers are positive non zero integers divisible by two. Zero is neither. -6 is neither. 5.3 is neither.

0 is neither. this is because 0 is not a number but instead it is the absence of a number. also 0 unlike integers does not have an assigned value or lack there of. Coming to the conclusion that 0 is not a number at all but instead is just a theory used to represent an idea that cannot be explained. :confused: a this is a complex thought but dont worry if you dont understand.

The definition of odd and even explicitly excludes zero. Now if you want to argue whether or not zero SHOULD be odd or SHOULD be even, then be my guess. But the issue here has already been decided.

also thoughs who refuse to believe me heres just an example of what i am like. first i am in 8th grade but am in geometry a 10th grade level math course. second, currently i have gotten nothing lower than one b on my math tests. third i am an unmeasurably gifted person and have been gifted with the pleasent capability of "deep thought"

There are different sets of numbers that build up to the Real Number system (the unique complete ordered field). Zero is an element of the set of Real Numbers, it's the "additive identity" -- the number that, when added to any other number x, doesn't change the value of x. (Similarly, 1 is the multiplicative identity -- the number that, when multiplied by any other number x, doesn't change the value of x.) So, zero is a number, just as any other element of the set of Real Numbers is a number.

Not all numbers belong to every set of numbers. Zero does not belong to the set of Natural Numbers (or "counting" numbers; ie: 1, 2, 3, ...), and zero does not belong to the set of Negative Numbers. Rather, zero belongs to the set of Positive (Non-Negative) Integers (0, 1, 2, 3, ...).

If you limit your definition of "number" to mean "natural number", then zero is not a number. The problem with that limiting definition is that fractions and negative integers would not qualify as numbers.

So, unless you're counting on your fingers (where, at least for the fortunate ones of us, fractions and negative numbers are absent), zero is a number.

But, obviously, multipying "0" by either a -1 or a +1 will still net you "0". It is neither positive nor negative. "0" is a neutral number.

I looked it up on Wikipedia NL and it says the even numbers are {0, 2, 4, 6, 8,...}, and the odd numbers can be written as 2n + 1 (which 0 can't). There's apparantly still a discussion going on in the scientific world about whether 0 is a natural number of not (but it is in any case a number) and there seems to be no general agreement about it. But Ribenboim states: "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 is an element of P."

I agree with Kreen, last year I was in 8th grade in geometry and now I'm a freshman taking algebra II Honors, 0 is neither odd nor even

"But, obviously, multipying "0" by either a -1 or a +1 will still net you "0". It is neither positive nor negative. "0" is a neutral number."

I meant to say that it is neither odd nor even. "0" is a positive number.

I looked it up on Wikipedia NL and it says the even numbers are {0, 2, 4, 6, 8,...}, and the odd numbers can be written as 2n + 1 (which 0 can't). There's apparantly still a discussion going on in the scientific world about whether 0 is a natural number of not (but it is in any case a number) and there seems to be no general agreement about it. But Ribenboim states: "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 is an element of P."
-3 * 2 + 1 = -5. Is -5 odd?

Well, the words HEAD and WALL :headbang: come to mind.

Numbers and mathematics was entirely created by man, and 0 was created to describe absence of anything

If you don't have any apples would you say it was odd or even? (Arguement for NEITHER)

-1 + 1 = 0

0 + 1 = 1

Therefore it seems logical to assume its EVEN (if we are talking on basic levels of mathematics, within constraints etc of certain branches of maths)

n / 0 creates problems however...

Thats my thoughts on the subject anyway... :rolleyes: It will never be proved either way...

EDIT: Just read Kreen's post, very interesting theory *thumbs up* :)

also thoughs who refuse to believe me heres just an example of what i am like. first i am in 8th grade but am in geometry a 10th grade level math course. second, currently i have gotten nothing lower than one b on my math tests. third i am an unmeasurably gifted person and have been gifted with the pleasent capability of "deep thought"
when you start doing calc based nuclear physics then you can brag but till then please dont

-3 * 2 + 1 = -5. Is -5 odd?
It is if negative numbers can also be considered as odd...

But I think 'n' can't be '-3' as it starts counting from 0

It is if negative numbers can also be considered as odd...

But I think 'n' can't be '-3' as it starts counting from 0
Isn't that kind of silly? If negative numbers can't be odd, and positives can, why can zero be even or odd, when it technically isn't positive (or negative).

0 is neither. this is because 0 is not a number but instead it is the absence of a number. also 0 unlike integers does not have an assigned value or lack there of. Coming to the conclusion that 0 is not a number at all but instead is just a theory used to represent an idea that cannot be explained. :confused: a this is a complex thought but dont worry if you dont understand.

also thoughs who refuse to believe me heres just an example of what i am like. first i am in 8th grade but am in geometry a 10th grade level math course. second, currently i have gotten nothing lower than one b on my math tests. third i am an unmeasurably gifted person and have been gifted with the pleasent capability of "deep thought"

Let me get this straight. We're supposed to take your word for this "complex" concept over at least two people with university degrees in the subject, one person who sounds an awful lot like a PhD student in mathematics, and a reasonable number of citations of authoritative sources? Like other people have requested, how about you post any published source for your belief?

If you don't think 0 is a number you simply don't get mathematics, whatever your grades.

Odd numbers are non zero positive integers not divisible by two. Even numbers are positive non zero integers divisible by two. Zero is neither. -6 is neither. 5.3 is neither.

Please state a source for your definition. Or accept the fact that you are incorrect.

zero is even. if you divide zero by two, you will get a whole number. it's like if you have two circles. and you have a bunch of apples. if you have an even number of apples, and you want to divide them equally into both circles, you won't have to cut an apple in half. If you have zero apples, then both circles get zero, no apple cutting. if you had 1 apple, you would have to cut the apple in half, therefore, 1 is odd.

how is this thread still going?????????

I think numbers are a social construct. They don't really exist except as part of mathematics, something made by humans.
As an abstract concept, you are correct. After all early mathematics served a practical purpose - how many chickens do I have or how many horses will it take to plow this field. In that context there are no abstract concepts such as zero or negative numbers. There is a leap in thinking to go from 4 chickens to 4 "things" to simply 4.

I don't know enough about math to offer an opinion to the question, but even as a non-mathematician I find this thread fascinating. My understanding of mathematics is more on the level of the historical developments and cultural contributions. Although ancient Mesopotamians and Babylonians had a punctuation-like notation to hold an empty place, the concept of zero as a number comes to us from India.

Interestingly enough its development was linked to religion, one of many examples of the connection between mathematics and religion. The first recorded use of the number zero is found as an inscription on a stone tablet from 876. The inscription is an equation determining how many flowers need to be planted in a specific space in order to provide a local temple with 50 garlands a day. The final numbers are denoted almost as they appear today although the 0 is smaller and slightly raised.

The Sanskrit word for zero, sunyam, becomes in Arabic sifr, from which we get the English cipher, which means having no influence or value; a nonentity.

Thanks, Right Thinking, for sending me on a little academic journey to find out more about zero.

P.S. I have a question for the mathematicians in the thread: What is zero divided by zero? I contend it is infinity, because to check the results through multiplication you can plug in any number and still get zero, but my wife insists the answer is zero, because any number divided by zero is zero.

The trouble is that if you divide 1 by any number and work down towards zero, you'll start getting larger and larger numbers and although you can't actually divide by zero you can say that 'the limit tends to infinity', meaning that it can't get higher than infinity. (Saying more than that would mean going quite deeply into what's meant by infinity, which is probably much more complex than what's meant by zero.) On the other hand, if you divide zero by any number and work that down towards zero, you'll keep on getting zero. So the problem is that where the two different patterns meet you have different things, so you can't say what the answer is.

In practice if you ever need to divide by zero it'll probably be because of a larger question like (x^2)/x, where x tends to zero. In that example you can still cancel the x's and get zero (there is a way to prove this, but it's fairly complicated). Other times you end up getting rid of the zero on the top by cancelling, for example if you had x/(x^2), and that would mean that the answer was indeterminable (infinite).

The trouble is that if you divide 1 by any number and work down towards zero, you'll start getting larger and larger numbers and although you can't actually divide by zero you can say that 'the limit tends to infinity', meaning that it can't get higher than infinity. (Saying more than that would mean going quite deeply into what's meant by infinity, which is probably much more complex than what's meant by zero.) On the other hand, if you divide zero by any number and work that down towards zero, you'll keep on getting zero. So the problem is that where the two different patterns meet you have different things, so you can't say what the answer is.

In practice if you ever need to divide by zero it'll probably be because of a larger question like (x^2)/x, where x tends to zero. In that example you can still cancel the x's and get zero (there is a way to prove this, but it's fairly complicated). Other times you end up getting rid of the zero on the top by cancelling, for example if you had x/(x^2), and that would mean that the answer was indeterminable (infinite).

So what is zero divided by zero?

Part 1:

Proposition: The number 0 is even.

For, as proof by contradiction, suppose that the number 0 is odd.

Then, 2k+1 = 0 for some integer k.
// Comment: this is by accepted mathematical definition, that you will find in any mathematical textbook. The term "integer" is used, and describes the set of numbers {..., -3, -2, -1, 0, 1, 2, 3, ...}. Therefore, by the accepted mathematical definitions of "even" (which is any number that can be represented by 2k, for some integer k) and "odd", any integer can be even or odd -- and, in fact, must be even or odd. This applies to the entire integer set and not just the natural set, not just the nonnegative integers -- the whole damn thing.
//

Then, 2k = -1.

Then, k = -1/2.

However, this is a contradiction, since k was supposed to be an integer.

Therefore, since the number 0 cannot be odd, the number 0 is even, q.e.d..



I will try and make this even more explicit.
Part 2:

Proposition: The number 0 is even.

For, as proof by contradiction, suppose that the number 0 is not even.

Then, 2k /= 0, for some integer k.
//Comment: I'm using the symbol "/=" to represent an equal sign with a slash through it, which means "not equal."
//

Then, k /= 0.

However, this is a contradiction, since 0 is an element of the integer set.

Therefore, etc, q.e.d..


If you try and refute this without bringing a valid mathematical citation to the table, you're a big fat idiot. You are not allowed to invent terms such as "neutral number." You are not allowed to use nonlogical reasoning that involves you doing well in high school mathematics.

You may, however, attempt to refute this in the form of a valid mathematical proof. Go ahead, try.

A news story from the German television news program (ZDF) "Heute" on Oct. 1, 1977:

Smog alarm in Paris: Only cars with an odd terminating number on the license plate are admitted for driving. Cars with an even digit terminating were not allowed to be driven. There were problems: Is the terminating number 0 an even number? Drivers with such numbers were not fined, because the police did not know the answer.