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Topic: Matheology § 258
Replies: 1   Last Post: May 3, 2013 3:09 PM

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Alan Smaill

Posts: 1,103
Registered: 1/29/05
Re: Matheology § 258
Posted: May 3, 2013 3:09 PM
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WM <> writes:

> No, that is a contradiction. First the set of natural numbers has
> cardinality aleph_0. Therefore it is actually infinite.


> Second the naturals are used to index the digits of the decimals. For
> that sake they are required to be actually infinite.

See your confusion revealed again:
the claim is that there is an infinite set.

There is no separate claim that "they" are required to be actually
infinite: you're revealing your underlying belief that classical
maths involves some mystical infinite natural numbers.

If you want to show the classical position is self-contradictory,
you should do as Russell did, and start from principles accepted
by current standard maths, and produce a proof from that.

> Regards, WM

Alan Smaill

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