It seems to me that the set of all numbers really used by mathematics and physics is countable, because they are defined by means of a finite set of symbols and, eventually, by computable functions.
Since almost all real numbers are not computable, it seems that real numbers are a set too big and most of them are unnecessary.
So why do mathematicians love this plethoric set of numbers so much?
Best Answer
It is much harder to avoid "unnecessary" real numbers than to accept them.