Does every mathematical operation has an inverse operation?

$\begingroup$

For example, we say that the addition and subtraction are inverse operations like that does each and every mathematical operation has an inverse operation?

$\endgroup$ 5

2 Answers

$\begingroup$

No. If you take the next "immediate" operation, multiplication, note that it doesn't always have an inverse, since division is not always defined. For instance:$$0\cdot 40=0\Rightarrow \frac{40}{0}=?$$Generically speaking (and this is by no means a theorem or an exact statement, only an intuition), "most" operations are not invertible, since you only need one element to not have an inverse in order to ruin everything.

$\endgroup$ $\begingroup$

Addition and subtraction have inverses if you only allow a single operand to vary (and fix the other one). But if you think of these operations as mapping an ordered pair of numbers onto a single number, then these operations don't have an inverse.

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy