Is zero positive or negative?

Follow up to this question. Is $0$ a positive number?

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This is not exactly a duplicate but has the same answer as in math.stackexchange.com/questions/18464/… – Mitch Mar 13 '11 at 14:52
The question is flawed. $\textbf{} \textbf{} \textbf{}$ – Bruno Joyal Oct 4 '13 at 3:03
Why does it have to be either positive or negative? – mez Jul 5 '14 at 13:16
youtube.com/watch?v=8t1TC-5OLdM – Arjang Oct 31 '14 at 1:49

It really depends on context. In common use in English language, zero is unsigned, that is, it is neither positive nor negative.

In typical French mathematical usage, zero is both positive and negative. Or rather, in mathematical French "$x$ est positif" (literally "$x$ is positive") allows the case $x = 0$, while "$x$ est positif strictement" (literally "$x$ is strictly positive") does not.

Sometimes for computational purposes, it may be necessary to consider signed zeros, that is, treating $+0$ and $-0$ as two different numbers. One may think of this a capturing the different divergent behaviour of $1/x$ as $x\to 0$ from the left and from the right.

If you are interested in mathematical analysis, and especially semi-continuous functions, then it sometimes makes more sense to consider intervals that are closed on one end and open on the other. Then depending on which situation are in it may be more natural to group 0 with the positive or negative numbers.

There are certainly much more subtleties, but unless you clarify why exactly you are asking and in what context you are thinking about this, it is impossible to give an answer most suited to your applications.

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To a computer programmer a significant context might be the IEEE 754 standard for floating point arithmetic, which distinguishes a +0 from a -0 representation. Of course mathematically there is only one Zero, but if your context is floating point representations, you could have it either way! – hardmath Mar 13 '11 at 15:05

No. $\textbf{} \textbf{} \textbf{}$

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Wikipedia is not the Holy Bible. Some people (like me) regard all Wikipedia content as false until proven correct. – Lisa Oct 30 '14 at 22:28
@Lisa then it's like the Holy Bible, for some (myself included) – Marc.2377 May 11 at 6:09
So what IS the Holy Bible / The Great Standardization Document of All Definitions for Mathematics? Because people are often fighting over different definitions of mathematical entities, 0 being one of such examples (French always start a flamewar when someone says 0 is not positive, because for French, 0 is positive and negative at the same time :P ). Same goes with definitions of angles, or square roots (only positive? positive and negative?) Being able to refer to some standard reference source with all the definitions agreed upon by the majority of mathematicians would be great. – BarbaraKwarc Jul 20 at 11:07

$0$ is the result of the addition of an element ($x$) in a set with its negation ($-x$). Hence, it is not necessary to conceive $0$ as having a negative element since it would produce itself. Therefore, by Occam's razor (i.e., the simplicity clause) it is not necessary for $0$ to have a negative element. However, by definition, the given set must have a negative element for all the positive elements. Therefore, it makes no sense to conceive it as a positive number.

Hence, $0$ is neither positive nor negative. That is intuitive since $0$ is null, defines nullity which is the absence of some abstract object.

However, if one does not agree with the simplicity clause, he can admit it as being both a positive and a negative number.

Therefore, as many things it is a matter of definition.

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Actually, zero is neither a negative or a positive number.  The
whole idea of positive and negative is defined in terms of zero.
Negative numbers are numbers that are smaller than zero, and
positive numbers are numbers that are bigger than zero.  Since
zero isn't bigger or smaller than itself (just like you're not
older than yourself, or taller than yourself), zero is neither
positive nor negative.

People sometimes talk about the "non-negative" numbers, and what
that means is all the numbers that aren't negative, in other words
all the positive numbers and zero.  So the only difference between
the set of positive numbers and the set of non-negative numbers is
that zero isn't in the first set, but it is in the second.
Similarly, the "non-positive" numbers are the negative numbers
together with zero.

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protected by Community♦Dec 10 '14 at 14:00

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