You in fact did write down "Graham's number" and "googleplex". Most real numbers cannot even be written down as a finite sequence of symbols in any way. However for algebraic numbers ("Plenty of irrational numbers"), every single one has a finite description.
There are uncountably many reals and only a countable number of "names" we can give them. This is a very real problem that makes people say that the real numbers are not real.
There are uncountably many reals and only a countable number of "names" we can give them. This is a very real problem that makes people say that the real numbers are not real.