# What's the terminology for whether a number is positive or negative?

Is there a word for the quality of a number to be either positive or negative? Consider this question:

What's the ... (sign/positivity/negativity, but a word that could describe either) of number x?

Also, is there an all-encompassing word for the sign put in front of a number (-5 or +5)? Word that describes both a plus and a minus sign?

• "sign"? ${}{}{}{}{}$ – Mariano Suárez-Álvarez Sep 10 '14 at 21:21
• "non-negative"? – Lehs Sep 10 '14 at 21:22

The word that you are looking for is the very word that you are using and that word is sign.

If you are looking for something more "academic", then you can use its Latin variant, signum.

Context can also effect what word you might choose. For instance, in physics it's common to use the word direction in place of the word sign.

But don't take my word for it, have a look at page $$229$$ of "A Handbook of Mathematical Discourse".

• "Sign" sounds so simple and non-academic, I'm looking for something different. – silkfire Sep 10 '14 at 21:32
• @silkfire But... it's the correct term. – user98602 Sep 10 '14 at 21:44

If you want to have a "less-simple" answer than the correct one given by @k170, the words positive and negative occur in all totally ordered commutative group with neutral element noted $0$. The positive elements $x$ are those for which $0<x$ and the negative ones are those such that $x<0$. The usual convention of the signs comes from $$x+(-x)=0$$ where $-x$ is the opposite of $x$. Given $x$ the positive part of $x$ is defined by $x_+=\sup\{x,0\}$ and the negative part is $x_-=\sup\{-x,0\}$ so you have $$x=(x_+)-(x_-)$$ Noting now $$|x|=\sup (x,-x)$$ (it is not an absolute value!) you have $$|x|=(x_+)+(x_-)$$ You can translate this to the numbers an take as convention (very useful!)the word "sign", positive or negative according to the involved element.

The search is for a PHILOSOPHICAL term to denote positive / negative. I agree that "sign" lacks something - hence, consider "polarity" and "charge".

• The term polarity applies to electricity, not math. – Shimmy Weitzhandler Apr 9 '18 at 14:00

It does help to have more specific technical terms like polarity, rather than sign, in the same way that it helps sailors to use port and starboard rather than left and right. The word sign IS correct, and it doesn't cause confusion like "left" would to sailors, but its many other common usages make it less valuable. (Also, people in any specialty have an almost compulsive need to abbreviate words that are common to their trade, and I believe this very human need to have a lingo is a coping strategy to help chunk large amounts of ideas and data.)