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?

**Answer**

It is much harder to avoid “unnecessary” real numbers than to accept them.

**Attribution***Source : Link , Question Author : Emilio Novati , Answer Author : Community*