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Topic:
Cardinality Question
Replies:
4
Last Post:
Jun 5, 2013 4:38 AM




Re: Cardinality Question
Posted:
Jun 4, 2013 5:46 AM


On 04/06/2013 10:40, ksoileau wrote: > Does anyone know whether \mathbb{R}=\mathbb{Z}^infty, i.e. do > the reals have the same cardinality as the collection of sequences of > integers? If so, where can I find a proof of this?
Yes. An amusing proof rests on the fact that continued fractions give a bijection between positive irrationals and sequences of positive integers.



