On 19 Jun., 14:12, Peter Percival <peterxperci...@hotmail.com> wrote: > mueck...@rz.fh-augsburg.de wrote: > > > Look: Zermelo has "proved" that the real numbers can be well-ordered. But it has been proved that the real numbers in fact cannot be well-ordered. That is as certain as that you cannot get a 13 with two dice. > > I think you're confusing two different results. There are models of ZFC > in which a well-ordering is a not definable. That does not mean that R > cannot be well ordered,
No, ZFC does not mean anything. It is simply fact that uncountably many reals cannot be names and, therefore, cannot be well-ordered. That is as factual as that you cannot get a 33 in roulette. Therefore scientists are very sceptical when a matheolgian announces that he has "proved" something. In general it is rubbish.