Is zero a positive integer? Could it be a prime number?

HallsofIvy

Elite Member
No, zero is not a positive number. Zero is neither positive nor negative. No, zero is not a prime number. No, "zero divided by zero" is NOT 0. It is 'undetermined'. a/b= c if and only if a= bc. If we claim that 0/0= c for some specific number, c, then 0= 0(c). But 0 times any number is 0.

tkhunny

Moderator
Staff member
Zero is not a negative integer, so is it positive?

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And could it be an even prime number? Zero divided by itself is zero, but zero divided by one is zero. So this confuses me.
There are programming languages that make various assumptions. Some tell you that 0/0 = 1 if it encountered in a program sequence. This is just an assumption of the code. It's not gospel. I think most of the time, if a program encounters 0/0, you will get either "NAN" (not a number) or a division error or something else catastrophic.

JeffM

Elite Member
Zero is not a negative integer, so is it positive?

View attachment 9533

And could it be an even prime number? Zero divided by itself is zero, but zero divided by one is zero. So this confuses me.
Consider red, blue, and yellow. Do you argue that a red ball is yellow because that ball is not blue? Consider the boundary line between Canada and the US: is it in Canada or the US or both?

Tell me what your definition of "positive" is, and I'll tell you whether or not zero is positive according to that definition. A common definition is that a number n is positive if and only if it is greater than zero and that a number is negative if and only if it is less than zero. Under that definition, zero is clearly neither negative nor positive. That is possible because, by definition, we have divided numbers into three classes rather than two.

If we do want to divide numbers into two classes, one way to do it is to define positive and non-positive numbers, in which case zero is non-positive. Or we can divide numbers into two classes as negative and non-negative, in which case zero is non-negative.

Pay attention to definitions.

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Jomo

Elite Member
Zero is not a negative integer, so is it positive?

View attachment 9533

And could it be an even prime number? Zero divided by itself is zero, but zero divided by one is zero. So this confuses me.
Zero is said to be a neutral number, neither positive nor negative. A positive integer n is said to be prime if the only positive integers that go evenly into it are 1 and the number n itself. Well 1, 2, 3, 4, 5, 6, ... all go evenly into zero so zero is the absolute worst candidate for being prime. 0/0 is not zero. 0/0 is indetermined. You really need to learn your definitions. Math is like a game where you can't play the game very well if you do not know the rules (definitions).

mmm4444bot

Super Moderator
Staff member
As JeffM wrote, definitions can vary.

I would say that most math courses treat zero as neither positive nor negative.

But, there are exceptions.

One example: electrical engineers sometimes treat zero as a negative number because it makes their life easier.