LudovicoVan
Posts:
3,004
From:
London
Registered:
2/8/08
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Re: Cantor's argument and the Potential Infinite.
Posted:
Nov 16, 2012 4:40 AM
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"Uirgil" <uirgil@uirgil.ur> wrote in message
news:uirgil-8D50A0.02310116112012@BIGNEWS.USENETMONSTER.COM...
> In article <k850hm$a03$2@dont-email.me>,
> "LudovicoVan" <julio@diegidio.name> wrote:
>> "Uirgil" <uirgil@uirgil.ur> 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?
-LV
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