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
- 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 (9.34 KiB) Viewed 98 times
- The First Two Lemmas Provide An Alternate Way To Prove That Two Functions Are Inverses Of Each Other If A Is A Set Def 2 (23.5 KiB) Viewed 98 times
Lemma 1. Suppose that f: A B and g: B→ A satisfy go f = id, and fog = ida. 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). Lemma 2. Suppose that f: A B and g: B→ A satisfy go f = idA, and fog = idg. Then g = f¹. Proof. You need to prove that g(b) <= a ⇒ f(a) work. = b. This should not be too much