- #1

Mr Davis 97

- 1,462

- 44

## Homework Statement

Prove that an endomorphism between two finite sets is injective iff it is surjective

## Homework Equations

## The Attempt at a Solution

I can explain this in words. First assume that it is injective. This means that every element in the domain is mapped to a single, unique element in the codomain, with no overlap. Since the domain and the codomain are the same size, this means that the map would have to be surjective. In the other direction, assume that the map is surjective, which means that every element in the domain must be associated with a unique element in the codomian. Since they are the same size, this the map is injective.

Is this acceptable? Is there a better, more mathematical way to come to these conclusions using the definitions of injective and surjective?

Last edited: