On Oct 29, 10:26 am, JRStern <JRSt...@foobar.invalid> wrote: > On Sun, 28 Oct 2012 15:25:27 -0700 (PDT), Arturo Magidin > > <magi...@member.ams.org> wrote: > >On Saturday, October 27, 2012 4:49:32 PM UTC-5, JRStern wrote: > >> Are there any such published? > > >You said elsewhere you are interested in "peer-reviewed" criticisms to > >Cantor's diagonal argument, but not from the point of view of intuitionism > >or some other logical framework, but strictly within the context of ZFC. > > >There are no such things, because the argument is a valid argument > >within ZF. It is in fact pretty short and clear. > > Then there can be a book taking on the objections one at a time and > knocking them down. > >
Using onto properties of functions is just double-talk reiterating the anti-diagonal method.
Proof. Let f:X->P(X) be a function.
This proves nothing about _enumerable_ sets!
This set of reals is _enumerable_ but it has 2 distinct _enumeration_ functions.