Applicability of Maths to the Universe

[Fireball]

This brings me to a somewhat related question I've had on my mind for a while. Why is it that such special numbers "found in nature" such as pi and e are irrational (and seemingly "arbitrary") as opposed to "clean" rational numbers? Is it to do with the particular number system being used (the decimal)?

Rationality is not affected by the number system used. A number is either rational or irrational. It is rational if it is a 'ratio' of two integers and irrational if not.

So, sqrt(2) is irrational. You cannot write it as ratio of two integers. The ancient Greeks knew this well before the decimal system for *describing* numbers.

Now, pi and e are more than just irrational; they are transcendental. In other words, they are not solutions of any polynomial with integer coefficients.

Well, it turns out that there are only countably many numbers that are *not* transcendental and uncountably many that are. So, in a sense, the vast majority of real numbers are transcendental. An 'arbitrary' real number is likely to be transcendental (and hence, irrational).

Bolding mine. Can you run that past me, but at a slow walk? I never would have thought that this would be the case. I suspect that if I go look it up in a text the discussion will be way over my head.