What is inverse in math terms?

Answer 1

In maths, the term there are two main meanings to the word inverse - both of which are very closely related. Simple answer in the last three paragraphs.

A binary operation, defined on a group of numbers is a rule that tells you how to combine two numbers to get a third. Each binary operations (@) has an identity element, generally denoted by i, such that:

x@i = x = i@x for all x in the group.

Then, for each element x, there is an element in the group, denoted by x-1 (or the inverse of x) such that x@x-1 = i = x-1@x

All this may sound rather technical. So here it is in simpler terms: two everyday examples of binary operation are addition and multiplication.

The identity for addition is 0. The identity for multiplication is 1.

The inverse of x, under addition, is -x. Under multiplication it is 1/x (not defined for x = 0).

These give rise to inverse binary operations: subtraction for addition and division for multiplication.