In comparing cardinal numbers we have set $|A| < |B|,$ if there is an injective, but no surjective function $f:A\to B$. This is motivated by a result by Georg Cantor (1845 - 1918) who realized that there is no surjective function between any set and its power set:

Proposition: Cardinals of a Set and Its Power Set

There is no surjective function between a given set $S,$ and its power set $\mathcal P(S).$


Proofs: 1

Proofs: 1

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  1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001
  2. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994