Uirgil
Posts:
185
Registered:
4/18/12


Re: Cantor's argument and the Potential Infinite.
Posted:
Nov 16, 2012 5:03 PM


In article <k851n8$fgs$1@dontemail.me>, "LudovicoVan" <julio@diegidio.name> wrote:
> "Uirgil" <uirgil@uirgil.ur> wrote in message > news:uirgil8D50A0.02310116112012@BIGNEWS.USENETMONSTER.COM... > > In article <k850hm$a03$2@dontemail.me>, > > "LudovicoVan" <julio@diegidio.name> wrote: > >> "Uirgil" <uirgil@uirgil.ur> wrote in message > >> news:uirgil981B6A.02055216112012@BIGNEWS.USENETMONSTER.COM... > <snipped> > > >> > ZFC offers a standard set theory in which actually infinite sets are > >> > not > >> > only allowed but actually required to exist, and no one yet has been > >> > able to show that ZFC is not a perfectly sound set theory. > >> > >> That is only because you are so incoherent as to insist to call N an > >> actual > >> infinity. > > > > In ZFC, the N is an actually infinite set. So until you can show that > > ZFC is internally inconsistent, which no one has yet done, we have > > actual infinities in ZFC. > > That's interesting: would you be so kind to show me how/why, technically > although informal as it needs be, N is an "actual infinity" in ZFC? > > LV >
ZFC requires the existence of a set N such that {} is a member of N, and If x is a member of N, so is x \/ {x}, and N is a subset of every set S such that {} is a member of S and If x is a member of S, so is x \/ {x}
Such a set is provably not finite, as finiteness of a set would require that it biject with some MEMBER of such an N, which N provably does not.

