In <firstname.lastname@example.org>, on 11/02/2012 at 05:48 AM, "Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> said:
>The proof moves from the assertion that there can be no list of Real >numbers to the assertion they are not countable. These are not quite >the same thing. There are countable sets (eg computable numbers) >which cannot be explicitly listed.
You are confusing constructability with existence. Cantor's results are not about constructability.
>Given that the inability to list a set even in principle is not >proof that it is uncountable, how does the proof go from 'there is >no list' to 'the set is uncountable'.
Because the definition of uncountable is that such a list does not exist.
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