Follow up to this question. Is $0$ a positive number?
Is zero positive or negative?
-
0https://www.youtube.com/watch?v=8t1TC-5OLdM – 2014-10-31
6 Answers
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.
-
0Some people (like me) might be looking for specific domains where people are concerned about the positivity of zero. A reasonable place to start is to search "strictly positive" or "strictly negative" in your favorite academic search engine. Those terms are used when there must be no ambiguity in whether or not a set of positive or negative numbers includes zero. I'd like criticisms of that search technique or other search suggestions if anyone has any! – 2017-03-17
No. $\textbf{} \textbf{} \textbf{} $
-
0I agree and favour the conventional *positive means positive*, i.e. *strictly* positive. – 2016-12-11
-
3So 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. – 2016-07-20
$0$ 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.
From : http://mathforum.org/library/drmath/view/58735.html
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.