Re: Uncountable sets in CZF?

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 20:59:04 +0200

raf@tiki-lounge.com (Ross A. Finlayson) writes:

> Cantor-Schroeder-Bernstein: it works both ways.
>
> What that means is that one of the reasons that people call the reals
> uncountable is because they've figured out a bijection between the
> reals and the powerset of the naturals, thus they reason that there
> are no bijections between the reals and the naturals, because
> Cantor-Schroeder-Bernstein says the existence of a surjection either
> way between two sets is proof of the existence of a bijection between
> those two sets.
>
> That is to say, the existence of a surjection from A to B and from B
> to A implies that A and B are equivalent, and as well from A to B to C
> and C to B to A through composition.
>
> That implies it is not a mathematical fact and to promote the other
> view as gospel, immutable, written in stone, etcetera, would thus be
> deceitful.

*What* implies *what* is not a mathematical fact? 

-- 
Jesse F. Hughes
"My baby don't allow me in the kitchen
   and I've come to love her decision."
                          -- Bad Livers

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