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, ...