How do we know numbers like “e” & “pi” are transcendental? If its true, how do people calculate all those digits of them, down to the millions of digits?

Question

Thank you in advance, im dumbfounded how we are able to calculate these numbers as if they are truely transcendental, there would be no way to express them as a true fraction.

In: Mathematics

Answer 1

The exact proof for either is about a full page of math.
But the general gist is:
If pi/e wasn’t transcendental, then there would be this way of representing pi/e in a not-transcendental way, and that it would have to match this other way of representing pi/e in a not-transcendental way.
And making them match is impossible.