I think the term of interest here is non-computable: irrational numbers can have finite kolmogorov complexity. You're kind of "begging the question" here, wher

I think the term of interest here is non-computable: irrational numbers can have finite kolmogorov complexity. You're kind of "begging the question" here, where you're assuming that non-computable numbers exist and then using that to show that some numbers are non-computable. You can definitely show that these things exist, but that relies on "believing" the set of axioms that you used to prove it.