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Topic: Cantor's first proof in DETAILS
Replies: 1   Last Post: Nov 17, 2012 2:29 PM

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Jesse F. Hughes

Posts: 9,776
Registered: 12/6/04
Re: Cantor's first proof in DETAILS
Posted: Nov 17, 2012 2:29 PM
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"Ross A. Finlayson" <> writes:

> The rationals are dense in the reals. So are the irrationals,
> nowhere-continuous, everywhere-dense, whose complement in the reals is
> each other: given those properties, they're indistinguishable.
> There's a contradiction either way - where the construction of the
> proof emphasizes one way, in vacuo, it's a plain claim.
> Then, there are reasonable definitions about our continuum of real
> numbers, to establish the standard and here extra the standard, where,
> the proof-theoretic constructs of the standard, do admit their own
> incompleteness.
> The conscientious mathematician is interested in the limits of the
> standard. Yes, the classical is perfect in the meso-scale, and as we
> know, there's more to it than that, for the grandest and most sublime
> of scales.
> Empty, it's as well a contradiction.

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