[mihvoi]

I only "believe" in the computable numbers - that can be defined by an algorithm at arbitrary precision.

That includes all rationals along with irrational that we have a way to approximate by algorithms - like sqrt(2) and PI. It does not include the incalculable numbers like Omega.

Being linked to algorithms, such numbers are only countable many, so they cannot contain "most" of irrational and therefore they lack most of "Real numbers".

There are mathematicians that take this view seriously, like "Constructivists" and "finitists". For example: https://www.youtube.com/watch?v=REeaT2mWj6Y