In article <firstname.lastname@example.org>, email@example.com wrote: > On Tuesday, 31 December 2013 17:08:54 UTC+1, wpih...@gmail.com wrote: > > > You think it is impossible to list all finite definitions? > > Yes, and so do you, > No. I have shown a list of all finite words.
No you have not.
WM has repeatedly denied the existence of any actually infinite lists, of which a list of all finite words would certainly be one, and now WM claims they actually do exist and that he has provided one of them.
WM blows hot and cold with the same breath!
> > since for a potentially infinite list, L, of finite > > definitions of potentially infinite 0/1 sequences there is a finite > > definition of a potentially infinite 0/1 sequence not an element of L. > > Any putative list you provide is a putative contradiction
> There is no difference with the list of all natural numbers.
Not every word names a natural number and not every natural number can be named by one world. While there may be a bijection between the SET of all natural numbers and the SET of all finite words, only WM would ever be so arrogant as to claim that every finite word IS a natural number and that every natural number IS a finite word. Everybody knows that WM is wrong.
> And in actual infinity of set theory: an infinite list has no finite > antidiagonal.
WM has no idea what goes on or does not go on with actual infinities. His mind is much too small.
Besides, no one other than WM himself ever claims finiteness for the number of digits of an antidiagonal, but its definition requires it to have a value between 0 and 1, which is eminently finite. --