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Re: Cantor's absurdity, once again, why not?
Posted:
Mar 14, 2013 6:15 PM


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 nonnameable numbers or unspeakable alphabets with unfindable characters are accepted, why should not also nonnameable natural numbers exist?
Regards, WM



