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

At least for pi there are people that figure out the new digits using super computers. There was recently 9 trillion digits new digits compute. So 31.4 trillion digits total. https://cloud.google.com/blog/products/compute/calculating-31-4-trillion-digits-of-archimedes-constant-on-google-cloud