- #1

scorpius1782

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## Homework Statement

Prove that if ##r : X \rightarrow A## is a retraction, then r is onto.

Please let me know if I did this correctly!

## Homework Equations

##i_A(x)=x## is the identity function of A

## The Attempt at a Solution

If 'r' is a retraction function then there is a function 's' such that ##A \rightarrow X## and ##r \circ s=i_A##

Then regardless of the input we put into ##r(x)## we will always get x out. Meaning that there is one, and only one, result for each element in 'r'. Then if 'r' is a function in ##\mathbb{R}## it will result in one output for each element in ##\mathbb{R}##.