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Topic: When has countability been separted from listability?
Replies: 22   Last Post: Oct 8, 2017 6:09 AM

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 bassam king karzeddin Posts: 1,662 Registered: 8/22/16
Re: When has countability been separted from listability?
Posted: Sep 30, 2017 10:34 AM

On Saturday, September 30, 2017 at 11:23:14 AM UTC+3, WM wrote:
> Cantor has shown that the rational numbers are countable by constructing a sequence or list where all rational numbers appear. Dedekind has shown that the algebraic numbers are countable by constructing a sequence or list where all algebraic numbers appear. There was consens that countability and listability are synonymous. This can also be seen from Cantor's collected works (p. 154) and his correspondence with Dedekind (1882).
>
> Meanwhile it has turned out that the set of all constructible real numbers is countable but not listable because then the diagonalization would produce another constructible but not listed real number.
>
> My questions:
> (1) Who realized first that countability is not same as listability?
> (2) Who has decided that this is not contradiction in set theory?
>
> Regards, WM

It seems that no one knows for sure, wonder!

BKK