Coming from a post on theydidthemath talking about Pi, all the top answers begin by explaining that **if** we consider Pi to be a “normal number”, then etc. They also mention we haven’t been able to prove whether it’s a normal number or not yet. What’s that about?
In: Mathematics
A normal number is one that contains all numbers in its decimal representation. The simplest normal number would be 0.123456789101112…
There is a belief that Pi is normal, though we aren’t able to prove it, which is where the “the works of Shakespeare are in pi” idea comes from.
Irrational numbers go on forever without repeating, but not all irrational numbers are normal, for example 0.13456789101113… will go on forever, but you will never find a 2
Edit: it’s not enough for all numbers (sequences of digits) to exist in the number, they need to have the same probability. My example happened to fit that but another example like 0.010203040506070809010011… would contain all numbers but not in equal probability, there are too many 0s, so it wouldn’t be normal. There are also complications with different bases but I’m not knowledgeable enough to comment on that, so my answer is only accurate in base 10
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