Let B be a set and let u, ve B. Then B {u} is equinumerous to...

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Let B be a set and let u, ve B. Then B\ {u} is equinumerous to B\{v}. Proof. Either u = vor u v. Case 1. Suppose u = v. Then B\ {u} = B\{v}. Hence B\ {u} is equinumerous to B\ {v}, by the reflexivity of equinumerousness. Case 2. Suppose uv. Then ve B\{u} and u B\{v}. Define h on B{u} by h(x) = bijection from B\{u} to B\{v}. if x = v; xifre B\{u,v}. {"2 Then h is a bijection from B\ {u} to B\{v}. Hence B\ {u} is equinumerous to B\{v}. Thus in either case, B{u} is equinumerous to B\{v}. B\ Let B, u, v, and h be as in Case 2 of the proof of Lemma Verify that h is indeed a Let B be a set and let u, ve B. Then B\ {u} is equinumerous to B\{v}. Proof. Either u = vor u v. Case 1. Suppose u = v. Then B\ {u} = B\{v}. Hence B\ {u} is equinumerous to B\ {v}, by the reflexivity of equinumerousness. Case 2. Suppose uv. Then ve B\{u} and u B\{v}. Define h on B{u} by h(x) = bijection from B\{u} to B\{v}. if x = v; xifre B\{u,v}. {"2 Then h is a bijection from B\ {u} to B\{v}. Hence B\ {u} is equinumerous to B\{v}. Thus in either case, B{u} is equinumerous to B\{v}. B\ Let B, u, v, and h be as in Case 2 of the proof of Lemma Verify that h is indeed a

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