Proof. If one has removed from T a finite number of   elements t1, t2,   …, tν−1 according to some rule,   then the possibility always remains of extracting a further   element tν. The set {tν},   in which ν denotes an arbitrary finite, cardinal number, is a   subset of T with the cardinal number ℵ0,   because {tν} ∼ {ν}. (Cantor 1895:   493)