In <k71vu3$cb7$1@news.albasani.net>, on 11/03/2012 at 02:35 AM, "Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> said:
>Obviously they are. Somebody constructs a list of purported Reals,
Nobody constructs anything. There is a universal quantifier, that's all.
>Cantor showed that the Reals are not recursively >enumerable, not that they are uncountable.
No, he proved that they are uncountable. Theories like ZFC may not be to your taste, but Cantor's proof is valid in them and nobody has ever found an inconsistency in them.
>The proof actually says that such a list cannot be constructed.
No, it proves that such a list does not exist, a stronger result.
>It starts with a hypothetical list that has already been >constructed.
It uses a shorthand notation for a longer expression involving universal quantifiers.
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