On 2010-06-21, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Actually, he shows that any purported list of all Reals must miss at last > one Real. > > *not* the same as being uncountable
Yes it is. Look up the definitions.
> witness the same argument applied to computable Reals.
Applying the same argument shows that any purported list of all computable reals must miss at least one real. So?
>> Actually Cantor's original "diagonal" proof was based on the set of >> all functions from the naturals to a two element set, > > No.
Yes, actually. There are many more modern reforumlations of Cantor's diagonal construction, and you are likely confusing those with the original. The more modern ones are more streamlined with the benefit of hindsight.
That is why you were asked by one poster *exactly which* version of Cantor's diagonal argument you are talking about. So far it seems to be a strawman proof you invented yourself and are ascribing to Cantor.