Virgil
Posts:
4,479
Registered:
1/6/11
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Re: Cantor's first proof in DETAILS
Posted:
Dec 9, 2012 10:41 PM
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In article
<72919023-5457-4eca-8d7c-31e93d64036d@r10g2000pbd.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:
> "There's no gap in this Heaviside step with connecting H(0+) and H(0-)
> with a simple line segment.
Since the H jumps from 0 to 1 at x = 0, tha segeemnt must have endpoints
(0,0) and (0,1),
The fiction being claimed to be continuous, for what x does the function
take the value 1/2?
> There is no point in it such that, not in
> the function, it is the only point in all neighborhoods of any [1] two
> points in the function, not in the function (not even a point
> discontinuity). Here "in the function" is each (x,y) in the combined
> coordinate image or co-range, with the function defined by the points
> in it.
I do not find enough sense in that to be worth its refutation.
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