> Do you plan on responding to my suggestion that you point out the > invalid step in Cantor's theorem? > > You say that Cantor's theorem is invalid, right? (You are using the > term "invalid" in its customary sense, I assume.) > > This means that there is some step in the argument which is invalid, > right? > > Would you like to step through the argument with me and show me which > step is invalid? >
You want some sport, but LV won't play?
> If so, how about I present the proof that, for any set X, there is no > surjection X -> PX, and you show me where that argument goes wrong?
Let me take his part.
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. 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'.
