> Of course, we don’t teach about computable numbers in school. Instead, the most common “upgrade” from ℚ are reals:

While "computable" numbers are a recent concept, already for a few centuries, since the early 18th century, mathematics has taught about another set of numbers intermediate between rational numbers and "real" numbers: the algebraic numbers, which are a subset of the computable numbers.

Like the "real" numbers, the "complex" numbers have also been partitioned since that time into "complex" integer numbers, "complex" rational numbers, "complex" algebraic numbers, "complex" transcendental numbers.

Everything that is now discussed in terms of "computable" and "non-computable" numbers, was previously discussed in terms of algebraic numbers and transcendental numbers.

While "computable" numbers is a more general concept that more precisely defines the limit between what is countable and what is not, the practical importance of this concept is reduced, because few of the computable numbers that are not algebraic are interesting, the main exceptions being the numbers that are algebraic expressions containing "2*Pi" and/or "ln 2".