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Topic: Cantor's argument and the Potential Infinite.
Replies: 17   Last Post: Nov 17, 2012 10:59 PM

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LudovicoVan

Posts: 3,206
From: London
Registered: 2/8/08
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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