Being rational means you’re a solution to a linear equation. sqrt(2) is irrational.
Being algebraic means you you’re a solution to an algebraic equation. Pi is transcendental, which means it’s not only irrational but non-algebraic.
Being computable means you can write a terminating program to compute the nth digit of the number. Pi is computable, I have no idea what isn’t computable.
But… just as naturals are countable, so are rationals, so are algebraic numbers, so are computable numbers. Which in turn means that the non-computable numbers that I can’t even describe are the VAST majority of numbers on the real number line.
Being rational means you’re a solution to a linear equation. sqrt(2) is irrational.
Being algebraic means you you’re a solution to an algebraic equation. Pi is transcendental, which means it’s not only irrational but non-algebraic.
Being computable means you can write a terminating program to compute the nth digit of the number. Pi is computable, I have no idea what isn’t computable.
But… just as naturals are countable, so are rationals, so are algebraic numbers, so are computable numbers. Which in turn means that the non-computable numbers that I can’t even describe are the VAST majority of numbers on the real number line.