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Unicity of Bijection

Proposition: If S is not empty and both f: N_n -> S and g: N_m -> S are bijections, then n = m:

(forall S != 0, n in N, m in N, f: Nn ->bijective S, g: Nm ->bijective S:

m = n).

Proof: see lecture notes.

The size of a set is uniquely defined.