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The previous concepts allow making a distinction between finite and infinite sets. In some literature, you will find this result not as a theorem, but as a definition of finite and infinite sets.

Theorem: Distinction Between Finite and Infinite Sets Using Subsets

Let $X$ be a non-empty set and $S\subset X$ its proper subset. Then

| | | | | created: 2019-09-07 15:20:26 | modified: 2019-09-07 16:18:44 | by: bookofproofs | references: [8297]

1.Proof: (related to "Distinction Between Finite and Infinite Sets Using Subsets")

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Bibliography (further reading)

[8297] Flachsmeyer, Jürgen: “Kombinatorik”, VEB Deutscher Verlag der Wissenschaften, 1972, Dritte Auflage