"Uirgil" <email@example.com> wrote in message news:uirgil-8D50A0.02310116112012@BIGNEWS.USENETMONSTER.COM... > In article <firstname.lastname@example.org>, > "LudovicoVan" <email@example.com> wrote: >> "Uirgil" <firstname.lastname@example.org> wrote in message >> news:uirgil-981B6A.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?