Follow up to this question. Is $0$ a positive number?
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.
$0$ 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.
protected by Community♦ Dec 10 '14 at 14:00
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