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Definition: Countable Set, Uncountable Set

A set \(D\) is called

1 This is equivalent with saying that there is a surjective function function \(f:\mathbb N\mapsto D.\) Some books define countability by requiring a bijective function between $D$ and $\mathbb N,$ but the above definition has the advantage that it is also applicable for a finite set $D.$ Thus, all finite sets are countable.

| | | | | created: 2014-07-11 21:08:10 | modified: 2019-01-26 11:11:14 | by: bookofproofs | references: [577]

1.Proposition: Union of Countable Many Countable Sets

2.Proposition: Real Numbers are Uncountable

3.Proposition: Uncountable and Countable Subsets of Natural Numbers

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Bibliography (further reading)

[577] Knauer Ulrich: “Diskrete Strukturen – kurz gefasst”, Spektrum Akademischer Verlag, 2001

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