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Re: Mathematics in brief
Posted:
Dec 8, 2012 5:49 AM
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On 8 Dez., 10:41, Zuhair <zaljo...@gmail.com> wrote:
I will give two answers, the first one depends on the finity of the
universe, the second one does not.
> Mathematics is "discourse
and discourse needs the tools available to us. They all are finite.
>
> How those forms are known to us? the answer is through their
> exemplification as part of the discourse of consistent theories about
> form.
Consistent means that discourse about all elements is possible.
We know that all finite words belong to a countable set. We know that
no infinite word can be mentioned without having a finite name.
Therefore this silly argument is really silly:
"I can decide for a real number x whether a real number y deviates in
its decimal (or any other) expansion from that of x."
The complete infinite expansion of x is never known, not even in an
infinite universe, but only the finite formula allowing expansion to
any required level.
So the argument is silly that there are uncountably many x because x
has an infinite expansion. No x is known without a finite formula,
name, word, ...
Regards, WM
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