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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: 2020-06-07 16:34:54 | by: bookofproofs | references: [577]