NationStates Jolt Archive

New thread started in response to a request from Ariarna when we had veered dangerously off-topic in the 'Book Burning' thread.

A quick blast of quoting to set up the background:

oh, and bwo - perhaps i should have said has the potential to hold three values. my point was that zero isn't a number, both minus one and one have a value though one is a negative value. it is still counted as existing in as valid a state as a positive number.

Hate to break it to you, but zero is a number and has a value which exists in as valid a state as either a postive or a negative number.

zero isn't a number it's the absence of value, the same as black isn't a colour it's the absence of colour

Wrong. Totally and utterly incorrect. Back to basic mathematics class for you.

Zero is a number, and it is not the absence of value, it is a definite value, and that value is null.

Take for example the set of all American Presidents that have been christened with the name "Fidel Castro". The number of members of this set is a definite value. That value is zero/null/cipher/0/nothing. There is no absence of value involved.

A simple web search will find ample reliable affirmation of the fact that zero is a number, and any negation of it is in error. For example, from the Mathworld Encyclopedia of Maths -

"Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. "

http://mathworld.wolfram.com/Zero.html

Edit: if you had any familiarity with Frege's 'Foundations of Arithmetic' you would realise just how ludicrous you claim that zero is not a number actually is, not only is it a real number, but it is the only number that can be used to generate all other numbers. It is the very basis of all number systems.

Added to which i'm using the word 'number' mean 'value' the same as i ment 'absence of reflected light on a particular wavelength' instead of colour.

But I will quite happily debate the existance of the 'value' zero with you if you want to post it. Perhaps you can explain to me why you can't square 1,3,5 and 7 even as a decimal place.

It looks to me like you are backpedalling here: you now claim that whenever you have used the term 'number' you have meant to use the term 'value'.

So, when you said "zero isn't a number it's the absence of value", you meant to say - "zero isn't a value it's the absence of value"?

Perhaps you can explain to me why you can't square 1,3,5 and 7 even as a decimal place.

I don't understand your question here. Are you asking why we can't square (ie. multiply by itself) or give the square root of those numbers?

I assume you mean give the square root, squaring them is trivially easy. (1, 9, 25, 49)

You are aware that the square root of 1 is 1?

Perhaps I have misunderstood.

Those two have no personality, do they?

Those two have no personality, do they?

I think you will find that the characteristic "pedantic and troublesome old git" qualifies as a personality...

...perhaps not a desireable one, but one none the less.

I think you will find that the characteristic "pedantic and troublesome old git" qualifies as a personality...

...perhaps not a desireable one, but one none the less.

Not so much of the 'old' you. I'm paranoid about my age enough as it is. I accepted long ago that i had no personality...or life...

Thats why I do philosophy... ;)

Anyway, i'm not back peddaling as much as saying i'm not using the words in there mathamatical sence, which i think is reasonable given we're not doing maths (as yet atleast), in there more commenly accepted verbal usage.

So, normal usage for expressing ideas;

Number \Num"ber\, n.

5. The state or quality of being numerable or countable.

8. (Gram.) The distinction of objects, as one, or more than
one (in some languages, as one, or two, or more than two), expressed (usually) by a difference in the form of a word;thus, the singular number and the plural number are the names of the forms of a word indicating the objects denoted or referred to by the word as one, or as more than one.

interestingly enough;

9. (Math.) The measure of the relation between quantities or things of the same kind; that abstract species of quantity which is capable of being expressed by figures; numerical value.

Here, 'number' means numerical value, therefore in using the word 'number' it can be read as 'value' anyway in a mathmatical sense, and what can we find for zero, (in a gramatical english viewpoint of course...;))?

Zero \Ze"ro\, n.;
1. (Arith.) A cipher; nothing; naught.

zero adj
1: indicating the absence of any or all units under consideration
3: of or relating to the null set (a set with no members)
4: having no measurable or otherwise determinable value

OK?
(ps. all quotes sourced from dict.org)

if you're talking mathemtics, then yes zero is a number as has already been explained. If you're talking real life, make your own mind up, i don't think it matters too much.

Strangely there is a very good book that actually discusses this...I think it's called the History of Infinity, very good...

In reality you are both wrong and correct at the same time,
there is actually a group of thought that says that all non-integers or integer ratios are not numbers...

In reality you are both wrong and correct at the same time,
there is actually a group of thought that says that all non-integers or integer ratios are not numbers...


However, 0 is an integer, so is unaffecetd by this debate.

I am unsure.
My educated guess would be that zero is a number that has no worth.

I am unsure.
My educated guess would be that zero is a number that has no worth.

Ack! must..not..get..dragged..into..boring..topic!

oh, one more post then, stupid me for doing a degree in maths...

no worth? do you mean it's not useful or it's value is nothing? because it is a very useful number indeed, much more useful than say... 142234.89.

Ack! must..not..get..dragged..into..boring..topic!

oh, one more post then, stupid me for doing a degree in maths...

no worth? do you mean it's not useful or it's value is nothing? because it is a very useful number indeed, much more useful than say... 142234.89.

Apologies, I will rephrase. I meant is a number with no value. I am sure it is very useful indeed.

Apologies, I will rephrase. I meant is a number with no value.

...but, it has a definite mathematical value... and that value is 0 (which is not the same as having no mathematical value).

I find it very odd that someone can believe that 1 and -1 have values, yet 0 doesn't.

Of course 0 is a number, even if it has no value. What I wonder more is, whether or not numbers are words.

Of course 0 is a number, even if it has no value. What I wonder more is, whether or not numbers are words.

Numbers are words, but what kind of words are they?

Are they Nouns? This is 3; 3 is a little shy, but very useful when you get to know...er...it.

Adjectives? I have 0 good to say to you.

Verbs? "Hey, what's 68 Plus 1?"

Or, are they letters? l33t sp34k f0r 3x4mpl3

Perhaps, punctuation marks? Yay!!!!1111

Numbers as such are Symbols, which are not words, just like letters are not words. Unless you spell out the symbol as in 7 = seven.

This sounds strongly similar to the argument that evil is merely the absence of god. Which is all bupkis considering that god is omnipresent. Anywho, back on topic. Of course it’s a number, and of course it has value. Where as the number one has a positive value, and the number negative one has a negative value. Zero will have a neutral value. To demonstrate my point further, lets change the scale to PH. Where six has an acidic value and eight has an alkaline value, seven will have a neutral value. Yet according to whoever those who think that zero isn’t a number would on this scale logically think that seven wasn’t a real number. Yet seven on a PH scale actually explains a little bit about a substance. It means that hydrogen and hydroxide ions are in a perfect balance with each other and probably a whole lot of other things that I’m not completely familiar with.

Now back to the zero scale. When performing an equation and the other values balance out so that the end result is zero, than what real value do any of the other numbers have if zero itself is not a real number?

Okay...
A discussion of whether or not zero is a Natural number*, I could understand, but whether or not it's a number, that's kinda pathetic. For a full proof, I'd need to get into different cardinalities of infinity, which isn't easy if you can't draw a graph, but here's a simple proof that doesn't require anything after basic geometry to understand.

Complex numbers are the combination of a "real number" and an "imaginary number," which is a number including i, the square root of -1. They are represented in a+bi form.
Both "real" & "imaginary" numbers are subsets of the set "complex numbers."
A real number, in it's proper form, is a+0i, and an imaginary number is 0+bi.
The polar opposite value (a for imaginary & b for real) must exist, else they would not be part of the subset of complex numbers.
Q.E.D.

While there are theoretically numbers outside the set "complex," you really, really, really do not want to get into that.
Furthermore, zero is (now) included in natural numbers, which is a subset of integers, which is a subset of real numbers.

*the answer seems to be "it depends on the book, but most everything originally written after 1960 says it is, as do about half before." Even beforehand, it was included in "whole numbers," still a subset of integers.