[FOM] Re: Excluded middle & cardinality of the reals

[Mark van Atten]

Andrej Bauer (Mon, 28 Jun 2004 09:32:03 +0200) asked:

> Perhaps someone out there knows: is there a known constructive proof
> that the set of reals (any kind of reals) is not countable?

If one thinks of the decimal expansions of the reals as choice sequences,
then
a continuity principle suffices to show that the reals cannot be enumerated.

Brouwer began using this argument as an alternative to the diagonal method
in his course on set theory of 1916-1917.

Mark.

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