Given f : E &#x2192;<!-- → --> E and f &#x2218;<!-- ∘ --> f = f .

Simone Werner

Simone Werner

Answered question

2022-05-21

Given f : E E and f f = f. Prove that if f is surjective or injective then f = I d E .

Answer & Explanation

aniizl

aniizl

Beginner2022-05-22Added 12 answers

Step 1
If f ( f ( x ) ) = f ( x ), then writing y = f ( x ), note the following:
Step 2
Then f ( y ) = f ( x ), and so by the fact that f is injective, y = x, or equivalently, f ( x ) = x.

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