On 20 Jun., 16:33, Newberry <newberr...@gmail.com> wrote: > On Jun 19, 6:06 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > Newberry <newberr...@gmail.com> writes: > > >> Because every infinite sequence of digits represents a real number? And > > >> the antidiagonal is one such sequence? > > > > If it does not exist then it does not represent anything let alone a > > > number. > > > > Now it is clear that it does not exist. Since all the reals are on the > > > list and the anti-diagonal would differ from any of them. This > > > violates the assumption. Hence the anti-diagonal does not exist. > > > Wow. Are you saying that the *sequence of digits* specified by the > > anti-diagonal does not exist? > > That's right. There is no formula or algorithm to construct the list. > It means that you would have to flip each and every digit one by one. > And that is impossible.
Well, there are some lists defined by finite definitions like 0.1 0.11 0.111 ...
But the number of these lists and the number of their diagonals is countable. > > > Anyway, in a sense, you're right. If we assume that every real is > > represented by a sequence on the list, then we can prove that every > > sequence occurs on the list (ignoring the issue of multiple > > representations). And yet, we can also show that a particular sequence > > is not on the list. > > Which sequence is that?
O, don't be unfair. Matheolgicians "prove" their claims. They are not used to give examples. Remember Zermelo who "proved" that every set can be well ordered. Although every sober mind today knows that hisproof is wrong, set theory is built upon this lie. Otherwise the hierarchy of infinities cannot exist.
Set-cranks suffer from selective damage of perception. There is no use to discuss with them. (Nevertheless we should go on as if they could understand - mainly to save those who have not yet become "mentally challenged zealots of abstract mathematics" (V.I. Arnol'd))