TITLE: Is there any number that I can't find?
QUESTION [19 upvotes]: I have a question that I think is quite weird and I can't find an answer. 
Is there any real number that I can't find using only $+,-,\times,\div,$ limits and radicals?
For example, using some series, I can find $\pi$ or $e$. But is there any number that I can't find using only those?
Sorry if I made any mistakes, I don't know how to ask that question or which tags to put.

REPLY [2 votes]: It depends upon what you mean by "number that I can't find", but there are an infinity of real numbers that you can't define in any way using what you are describing.
Consider the set of numbers you can "define". The definition of such a number is some kind of text you can encode as a binary number, so this set is a countably infinite set. 
Because real numbers are uncountable, there is an infinity of real numbers you can't define.