The continuum problem and forcing
Cantor introduced two fundamental ideas in the theory of infinite sets: he discovered (or invented?) the scale of cardinalities of infinite sets, and gave a proof that this scale is unbounded. We recall that two sets M and N are said to have the same cardinality (card M = card N) if there exists a one-to-one correspondence between them. We write card M⩽ card N if M has the same cardinality as a subset of N. We say that M and N are comparable if either card M ⩽ card N or card N ⩽ card M. We write card M > card N if card M ⩾ card N but M and N do not have the same cardinality.
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