LudovicoVan
Posts:
4,067
From:
London
Registered:
2/8/08


Re: The selfcontradictory infinite hotel
Posted:
Feb 24, 2014 4:15 PM


"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote in message news:leefm0$j54$1@news.albasani.net... <snip> > The natural integers are infinite: there is no greatest, this is via > induction. Then, Goedel proves the consistent arithmetic > incomplete, there are true facts about its objects, only integers, > and consistent thus with all other true facts, that are not theorems > already of "there are only finite(ly) many integers that are > infinite". Then, there are infinitely many integers that are > infinite, this with that there are still only integers. > > Then, for what infinity is or would, it is symmetric to zero that > all its predecessors reflect and go to zero as all zero's successors > go to it.
But that's exactly my bottom line: there is no infinity popping up from the simply endless, instead already and since the start an infinite set is *extended*, i.e. includes its infinities. Hence, it's you (and the standard) here who do not take your conclusions to their full premises...
Julio

