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

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Robin Chapman

Posts: 296
Registered: 5/29/08
Re: Cardinality Question
Posted: Jun 4, 2013 5:46 AM
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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.




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