>>12389137While that is true for a general "real" number, it's not true for pi. Pi is not actually a number, it's a "metanumber". It has very nice properties, a nice finitistic description and an algorithm to compute it, which makes it extremely special and nothing like the vast majority of other "real" numbers.
Having these properties means you can also prove cool theorems about this pi in a totally unique way using this description (which is completely impossible for most other numbers).
This is also why so few irrational numbers are known. There are a few theorems that give you some cool relatively large classes of irrational/transcendental number, but still they are quite contrived and for a general "real" number you come up with you will have no way to prove that it's irrational.