[robinhouston]

A rather more technical – but very interesting – take on this question is [0], which opens:

> One occasionally hears the argument — let us call it the math-tea argument, for perhaps it is heard at a good math tea — that there must be real numbers that we cannot describe or define, because there are are only countably many definitions, but uncountably many reals. Does it withstand scrutiny?

then explains in detail why it does not withstand scrutiny.

[0] https://arxiv.org/abs/1105.4597