On Jun 9, 12:42 am, George Greene <gree...@email.unc.edu> wrote: > > "William Hughes" <wpihug...@hotmail.com> wrote > > > Is this digit sequence (which does not have a last 3) > > > > 33333... > > > > in this list > > > > 1 3 > > > 2 33 > > > 3 333 > > > ... > > > > of sequences (all of which have a last 3). > > > > Yes or No. > > I said it first. > > Herc replied (astoundingly) > > > No. > > If you actually believe this, then why do you keep talking about how > having "every digit sequence" MATTERS? THIS LIST HAS EVERY > digit sequence, up to EVERY finite length, MATCHING .33333.... ! > NAME ME ONE POSITION where this list of FINITE strings DOESN'T MATCH > .3333.....! YOU CAN'T!! Yet DESPITE this, .3333.... IS NOT ON THIS > LIST! > YOU YOURSELF JUST SAID SO! >
Indeed, and you agreed. There existing some position where the initial part of X does not match any of the Y's is not the only way that X can differ from every one of the Y's .
> So why are you having so much trouble noticing that EVEN if you have > EVERY possible FINITE initial sequence somewhere on your list of > computable reals, you still DON'T have many infinite ones (and you > provably do NOT > have the infinite anti-diagonal, since that PROVABLY DIFFERS from > EVERYthing you DO have > on the list!)?
I am not having any trouble. The infinite anti-diagonal is a "new string". It is a string missed by the list. The list does not contain every possible string. The fact that
All possible digit sequences are computable to all, as in an infinite amount of, finite lengths.
does not mean there is a list where Cantor's argument fails.
