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.
> 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?
> This is a contradiction and hence *our assumption* > that every real is represented by a sequence on the list must be false. > > You've never seen proof by contradiction in your life? How remarkable. > > -- > Jesse F. Hughes > > "Of course, I don't need any more education." > -- Quincy P. Hughes (age 7)
