For English language learners that actually want to know, this doesn't work because "real" and "rational" are adjectives to the noun "numbers."

The word "numbers" is countable, evidenced by it being plural, so we would still say "many real numbers." The adjective does not change the countability of the noun. For example, "How many infinite things are there?" The adjective "infinite" does not change the fact that the word "things" is countable.

Linguistics cares not for mathematical rigor. Math is solid and constant. Linguistics flows and changes over time such that in enough generations everything I've said might become incorrect. Trying to pin one of these to the other is silly.