Give a bijection between two sets

Asked Mar 28 '17 at 16:54

Active Mar 28 '17 at 16:54

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The two sets are the following: $(0,1) $ and $ [0,1]$

I know that (the cardinality of) $|(0,1)|=| \mathbb R|$ so it has to be true, that $[0,1]=| \mathbb R |$

Can I maybe use Hilbert's paradox of the Grand Hotel, or should I found a function, which Domain is $(0,1)$?

asked Mar 28 '17 at 16:54

Zauberkerl

As reference, http://math.stackexchange.com/questions/2204690/find-a-bijection-f0-1-rightarrow0-1/2204720#2204720 – Jacky Chong Mar 28 '17 at 16:57
If you know their cardinalities are both equal to $|\mathbb{R}|$, you can just compose the bijections which let you know this fact. – Patrick Stevens Mar 28 '17 at 16:58
I know their cardinalities, but I can't prove it – Zauberkerl Mar 28 '17 at 16:59
Also, more or less everything on this page: http://math.stackexchange.com/questions/linked/160738 – Asaf Karagila Mar 28 '17 at 16:59
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@AsafKaragila Oh my! That is a popular question! :) – Bram28 Mar 28 '17 at 17:39

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