eli5, is it true that irrational numbers like pi contains every single number combination in it?

Question

eli5, is it true that irrational numbers like pi contains every single number combination in it?

In: 0

Answer 1

For some irrational numbers, no, the digits don’t repeat but also are not in a random uniform distribution. For example,

1.0110111011110111110…

is irrational but has only 1s and 0s.

The digits of pi are thought to be randomly uniformly distributed, and so you would expect to find any given finite sequence somewhere in it, but it hasn’t been proven. And that’s because if you randomly select N digits an infinite number of times (which pi is thought to do), you will eventually get every sequence of N digits.