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Re: Cantor's absurdity, once again, why not?
Posted:
Mar 14, 2013 6:15 PM
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On 14 Mrz., 22:03, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> Let me ask you about this notion of falsifiability. I presume that
> you'd agree that Fermat's theorem,
>
> (An > 2)NOT(E a,b,c)( a^n + b^n = c^n )
>
> is falsifiable, since if it is false, we can show that it is false by
> producing n, a, b and c such that
>
> n > 2 and a^n + b^n = c^n .
>
> So that is a proper mathematical statement (or whatever), right?
This is trivial enough for you to understand.
Obviously it is above the horizon of many matheologians to understand
that |R| > |N| bears a contradiction, since elements of a set must all
be distinguishable, that means definable by finite words, but as can
be shown in ZFC, there are not more than countably many finite words.
I don't understand why that is more difficult to understand than the
proof that n > 2 and a^n + b^n = c^n is impossible.
At least if non-nameable numbers or unspeakable alphabets with
unfindable characters are accepted, why should not also non-nameable
natural numbers exist?
Regards, WM
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