> 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. >
Sorry, but the proof commences with a purported list of all Reals. Look at it.
> > 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,
Ohh no, that's definitely false.
> but Cantor's proof is valid in them and nobody has ever > found an inconsistency in them. >
The proof we are discussing is not formulated in the language of ZF. The equivalent proof in ZF is correct.
> > The proof actually says that such a list cannot be constructed. > > No, it proves that such a list does not exist, a stronger result.
By showing any purported list is missing a Real.
> > > It starts with a hypothetical list that has already been > > constructed. > > It uses a shorthand notation for a longer expression involving > universal quantifiers.
That's the source of some of the problem in the proof - it uses a shorthand which isn't quite correct and isn't properly explained.
I have no problem with the very similar proof in ZF.
