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The first two lemmas provide an alternate way to prove that two functions are inverses of each other. If A is a set, def
Posted: Mon Jul 11, 2022 12:04 pm
by answerhappygod
- The First Two Lemmas Provide An Alternate Way To Prove That Two Functions Are Inverses Of Each Other If A Is A Set Def 1 (18.08 KiB) Viewed 54 times
The first two lemmas provide an alternate way to prove that two functions are inverses of each other. If A is a set, define the identity map on A by id: A → A, id,(a)= a. Then id, is clearly a bijection. Lemma 1. Suppose that f: AB and g: BA satisfy go f = id, and fog= idg. Then f and g are bijections. Proof. Hint: By symmetry you can just prove that f is a bijection. Do this directly from the definitions (don't quote any other results).