Hi,
Le Friday 21 December 2007 13:08:38 Günther Greindl, vous avez écrit :
> Hi Russell,
>
> Russell Standish wrote:
> > In your first case, the number (1,1,1,1...) is not a natural number,
> > since it is infinite. In the second case, (0,0,0,...) is a natural
> > number, but is also on the list (at infinity).
>
> Why is (1,1,1,...) not in the list but (0,0,0,...) in the list at
> infinity? This seems very arbitrary to me.

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Because zero even repeated an infinity of time is zero and is a natural
number. (1,1,1,...) can't be a natural number because it is not finite and a
natural number is finite. If it was a natural number, then N would not have a
total ordering.
> I am becoming more and more an ultra-finitist. Arguments with infinity
> seem to be very based on the assumptions you make (about platonia or
> whatever)
Finite and infinite concepts are dual concepts you can't leave one without
leaving the other.
> Regards,
> Günther
Regards,
Quentin Anciaux
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