[TuringTest]

No, there are also non-computable numbers that are imaginary, complex, or transfinite.

[pcvarmint]

All rational numbers are real. Therefore all non-real numbers are irrational.

[TuringTest]

Uh, no, "irrational" is defined as a subset of real numbers.

[pcvarmint]

Non-rational, then.

This is about as consequential as debating whether 1 is a prime number.

[TuringTest]

This thread was about "all the numbers that it's theoretically impossible to compute". If you think the difference between "irrational" and "non-rational" in this context is irrelevant, you have a weak grasp of number theory. Yes, all are non-computable, but in different ways.