"Peter Webb" <webbfamilyDIEspamDie@optusnet.com.au> wrote in message news:email@example.com... > Jesse F. Hughes wrote: > >> 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'.
You seem frustrated. I have already referred to the links I have (already) posted up-thread. What is it that you still do not understand?