NationStates Jolt Archive

For all those who thought they could come in here and blast some idiot who thinks that the integer 0 isn't even consider this:
Let O:R->R be defined by O(x)=0 for all x in R (the zero function)
then O is odd:
O(-x)=-O(x)
and O is even
O(-x)=O(x)
Therefore zero is both odd and even. QED

Too bad someone who doesn't know what he's talking about is going to post something that makes no sense and ruin my first thread.

For all those who thought they could come in here and blast some idiot who thinks that the integer 0 isn't even consider this:
Let O:R->R be defined by O(x)=0 for all x in R (the zero function)
then O is odd:
O(-x)=-O(x)
and O is even
O(-x)=O(x)
Therefore zero is both odd and even. QED

Too bad someone who doesn't know what he's talking about is going to post something that makes no sense and ruin my first thread.

As in number theory we are taught the origin (0) is a special case neither odd nor even but with some properties of each depending on application

For all those who thought they could come in here and blast some idiot who thinks that the integer 0 isn't even consider this:
Let O:R->R be defined by O(x)=0 for all x in R (the zero function)
then O is odd:
O(-x)=-O(x)
and O is even
O(-x)=O(x)
Therefore zero is both odd and even. QED

Too bad someone who doesn't know what he's talking about is going to post something that makes no sense and ruin my first thread.
You are confusing "function" with "number." Just because the 0 function displays properties of both odd and even functions doesn't mean the number 0 is both even and odd. To disprove your method, we can take for example f(x) = 3 which is an even function but this does not show that 3 is an even number. 0 is an even number because all even numbers n must display the property of n = 2m where both n and m are integers. Since 0 = 2(0), 0 is even.

But there is no three function. If you look at R and C(R) as vector spaces both zero and the zero fuction, respectively, play the role of the additive identity.

Here is some info I found on it
http://mathforum.org/library/drmath/view/57188.html

But there is no three function. If you look at R and C(R) as vector spaces both zero and the zero fuction, respectively, play the role of the additive identity.


You're making false analogies between numbers and functions.The function still doesn't show how the number is even. Consult any mathematics resource and it will tell you 0 is exclusively even.

Zero is a neutral number. I displays no characteristics of even, odd, positive, or negative integers. And notice, it is also placed at the exact center of a standard cartesian plane.

Since there is no other numerical value that shares properties with zero, it is not considered part of any ordered graphable set that contains numerous numbers and therefore, is the only neutral number.

In the immortal words of Ebaumsworld...

WTF, Mate!

Zero is a neutral number. I displays no characteristics of even, odd, positive, or negative integers. And notice, it is also placed at the exact center of a standard cartesian plane.

Since there is no other numerical value that shares properties with zero, it is not considered part of any ordered graphable set that contains numerous numbers and therefore, is the only neutral number.
Lol you sound just like me in the 2nd post that no one payed attention to :D lol

Zero is a neutral number. I displays no characteristics of even, odd, positive, or negative integers. And notice, it is also placed at the exact center of a standard cartesian plane.

Since there is no other numerical value that shares properties with zero, it is not considered part of any ordered graphable set that contains numerous numbers and therefore, is the only neutral number.
Zero is even because it displays the property of all even numbers n: n = 2m, where n and m are both integers. 0 can fit this condition by the relationship 0 = 2(0)

In the immortal words of Ebaumsworld...

WTF, Mate!
Just for clarification Ebaumsworld didn't make "The End of the World", it was created by Fluid. Ebaumsworld justs steals content from other people and credits it as their own.

For all those who thought they could come in here and blast some idiot who thinks that the integer 0
For all those who don't get it, this is a joke. I have made no false analogies, and I never claimed that 0, the integer, isn't even. I am just poking fun.

Zero is even because it displays the property of all even numbers n: n = 2m, where n and m are both integers. 0 can fit this condition by the relationship 0 = 2(0)


zero can fit any condition where multiplication is involved. An even times an odd will always equal an odd - correct?

so, 0 = 3(0) would seem to say it is even.

But wait. An odd times an odd is even. Lets place zero as an odd

0 = (0)(7)

apparently we have too odd numbers equalling another odd number.


My base point is this: zero is a neutral number because you can use to prove either even or odd notation.

Zero is a non-integer. It is nothing.

I'm just curious where you get this logic?

An even times an odd will always equal an odd - correct?
Try 2x5=10 , 12x9=108 , 4x27=108 (and many more)

An odd times an odd is even.
Actually an odd times an odd usually makes an odd answer.
Such as 7x7=49 , 13x3=39 , 15x17=255 (the list is virtually endless)

zero can fit any condition where multiplication is involved. An even times an odd will always equal an odd - correct?
even * odd always equals even.

so, 0 = 3(0) would seem to say it is even.

But wait. An odd times an odd is even.
odd * odd is always odd.

Lets place zero as an odd

0 = (0)(7)

apparently we have too odd numbers equalling another odd number.
You are using incorrect circular logic by defining even numbers in terms of even numbers and defining odd numbers in terms of odd numbers. This will reveal nothing and can lead to erroneous conclusions. For example, with your explanation, one can argue that 1 is even because 1 * 1 = 1, and this will fulfill the rule that even * even = even. 1 is obviously not even because the conditions for "evenness" and "oddness" are based on other factors, not on this circular type logic.

My base point is this: zero is a neutral number because you can use to prove either even or odd notation.
THe multiplication relationships you mentioned are logical progressions from basic definitions. and somewhere in your logic there is a mistake made when you flip the logical progression and try to derive basic definitions from the multiplication relationships. this can lead to problems, such as defining 1 as even. The correct notation for even and odd numbers is this: "Odd numbers" r satisfy the relationship r = 2m+1 where r and m are integers. 0 is therefore not odd. "Even numbers" n satisfy the relationship n = 2m where n and m are integers.

I don't think there is such a thing as "neutral numbers." Look up any mathematical resource in the world and it will tell you that odd numbers are (...-3, -1, 1, 3, 5...) and even numbers are (...-4, -2, 0, 2, 4...).

Zero is a non-integer. It is nothing.
actually zero is an integer.

0 is round

My base point is this: zero is a neutral number because you can use to prove either even or odd notation.Erm... The Def'n of "odd" is :"satisfies the equation 2*I+1 for some I is an element of the Integers"

Whereas even, is "2*I..." So, whether or not I is an element of the integers, or whether or not is can be used as an integer, for the Def'n of "even" given to prove all physical (up to and including Calc) math, then 0 is even.

Whether it would be even to someone who can understand what a Lebesque intergral is, I can't tell you, because that is (very temporarily) beyond me, but for all purposes which would affect a person who doesn't have to deal with proving things even I have never heard of (which includes quite a bit, I will admit), it is functionally even.

I'm just curious where you get this logic?


Try 2x5=10 , 12x9=108 , 4x27=108 (and many more)


Actually an odd times an odd usually makes an odd answer.
Such as 7x7=49 , 13x3=39 , 15x17=255 (the list is virtually endless)

sorry, reverse those. I'm being stupid tonight.

Oddness and evenness with respect to functions have precisely nothing to do with the oddness and evenness of integers. Odd functions are symmetric with respect to the the origin and even functions have symmetry with respect to the y-axis. Odd integers leave a remainder when divided by 2, even integers are evenly divisible by 2.

Since 0/2 = 0, which is an integer, 0 falls into the category of even integers.

Of course, the zero function, which takes every real number to zero, is of course both even and odd as you showed.

But your claim does point out an interesting possible point of confusion. So all in all, I guess I do see the humor in it after all. :cool:

actually zero is an integer.
I was speaking metaphorically. But, just try to divide by it.