# What's the word for converting a positive number to negative one and negative to positive?

What's a good word to describe the operation of taking the negative of a number? For example, given `x = 5`, obtain `-x = -5`, and given `y = -2`, obtain `-y = 2`.

Is there a word for this?

I was thinking about "negation" or "negate". But according to M-W, it means:

to cause (something) to not be effective

grammar : to make (a word or phrase) negative

It doesn't seem to cover "to make a number negative".

• I think this would normally be referred to as "changing the sign" or "reversing the sign" of the number. – Max Williams Jun 24 '16 at 16:21
• The usage of "negate" is usually synonymous with "cancel out", which is closer to "make zero" than it is to "make negative" (in a non-mathematical context, that is). – Max Williams Jun 24 '16 at 16:25
• @MaxWilliams Thanks for your help. I agree. On the other hand, I was hoping for a single word/noun to use in a title. – tinlyx Jun 24 '16 at 16:29
• The word in math is "negate". Your dictionary is not giving you the meaning in a math context. Negating a number returns its additive inverse. – Drew Jun 24 '16 at 17:25
• "Inverting the sign" is another option. – Hot Licks Jun 24 '16 at 17:31

## 3 Answers

Negation absolutely is is the correct term to use here: it is a synonym of "additive inverse", as noted in the second sentence of its Wikipedia article. This is a well-defined mathematical operation which would absolutely be understood in a numeric context, and is used constantly in math classes from grade school through Master's programs; the dictionary just wasn't providing the domain-specific definition of the term.

The action would be called "Finding the additive inverse" of the number.

The additive inverse is the number that, when added to your initial number, adds up to zero.

There are other possible terms in the Wikipedia excerpt below

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number), sign change, and negation. For a real number, it reverses its sign: the opposite to a positive number is negative, and the opposite to a negative number is positive. Zero is the additive inverse of itself.

Of note is "opposite number".

The opposite of a number is just the number on the opposite side of zero on the number line.

• While it might be tempting to reduce the term to "inverse", this becomes unclear as there is also a multiplicative inverse, also known as the "reciprocal". – Catija Jun 24 '16 at 17:15

This isn't quite as simple as you might think. There is more than one way to get from A to B. This lack of uniqueness is one reason there isn't a single word for the process. You can multiply by -1, or subtract from 0. But what is -1, other than 0 - 1. So it looks like a subtraction operation, except that it is given an order of precedence above ordinary subtraction in common written and computer syntax. So it tends to be treated as a distinct operation. If you need a name for the result, negation is as good as any. However, if you need to make the distinction between the names of the logical (Boolean) and mathematical operators that perform negation, you need two different names, such as minus and not. linky to example usage in Wikipedia

## protected by Community♦Jun 3 '17 at 13:11

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