Is Zero a Whole Number?

Absane said:
No... zero is called "neutral." It's the only number where -x = x.. x + x = x.. x - x = x... ect.
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Where is it shown that zero is "nuetral"?
 
Fafnir665 said:
Where is it shown that zero is "nuetral"?
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It's the result of the definitions of positive and negative numbers.

x is positive if and only if x > 0
x is negative if and only if x < 0

If x = 0.. what do you call it? Make up another definition.. It's how mathematics works. Just like for sets. Like this one: You have some long winded definition of a finite set... then you simply say: if the set S is not finite, then it's infinite.

Just how things are done.
 
I've taken course up to calculus, and I've never once heard someone refer to zero as 'nuetral,' so what youre saying is you just made up that qualification for the number?
 
Fafnir665 said:
I've taken course up to calculus, and I've never once heard someone refer to zero as 'nuetral,' so what youre saying is you just made up that qualification for the number?
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Maybe I did make up the qualification? But two things: 1) I did not make up the definition of positive and negative numbers. 2) I have heard others say zero is neutral. I would agree with number 2 because the definition of the word itself matches what zero falls between.
 
I just wont agree that there is a mathmatical application for the word 'nuetral', it makes a nice description of the number zero because -0 = 0.
 
Well then pick your own word. It's easier than saying "zero is neither negative nor positive."
 
The definition in group theory is that an additive identity is any z such that:

z + x = x = x + z, for all x in the group.
 
What? This is the definition of neutral? Or what? Anyway for the group (R,+), z = 0. For the group (R, *), z = 1.
 
Nevermind.. you are correct. It's also called the "identity element." But the IE differs between + and *. But zero is neutral for addition on R.
 
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