On Saturday, 22 March 2014 22:50:53 UTC+1, Virgil wrote: > In article <email@example.com>,
> Why should anyone else be required by WM to do what WM himself CANNOT > do, or at least never has done. namely successfully defend his own idiot > assertions.
You are right that I never defended idiot assertions. But Dan has claimed that he can. >
> The Peano postulates are accepted by the vast majority of mathemaicians > in the world as being the skeleton of mathematical induction and that it > is by such an induction that the we;;-ordered set of natural numbers is > defined.
That has been mentioned here frequently, but it is not an argument. It is obvous to everybody whose brain has not been perverted or deleted completely that the Peano axioms do not define the natural numbers.
In principle it is without interest whether you understand that. But this discussion is a splendid demonstration of the fact that ridiculous but not so obviously foolish ideas like uncountable sets and undefinable numbers can exist in "modern mathematics".