The infinite digits of pi that we don't know. But we do know that they exist, so pi, or any other irrational number, will aptly be called a "known unknown."
> Virtually all numbers are irrational.
For every n irrational numbers you name, I can name n+1 rationals. There is no firm basis to the argument that there are somehow more irrational numbers than rational numbers.
I think Cantor can rest peacefully.
It's a bit suspicious that we can't name or describe any of the uncountable irrational numbers, isn't it? Not even a single example.
Cantor's proof is not constructive. It doesn't name an example. If you enumerated all irrationals based on the algorithm required to calculate them then the contradiction in Cantor's diagonalization proof just turns into a failure to terminate. But that suggests that there are fewer irrationals than integers, not more.
I name "x+pi for every rational number x". Good luck!