[gorgoiler]

Is this correct, mathematically?

I understand the point that PI contains every possible piece of information, theoretically.

However, the chance of finding a given string in PI depends on the string’s length. The longer the string, the more the probability tends to 0.

The paradox therefore is that PI contains every PDF, but you will never find them, so in what sense does it really contain them at all?

[lsiebert]

No, all strings theoretically exist in 𝛑 given enough digits, so longer strings don't reduce probability of existence, they just mean that it will take more digits to find them.

[tsbertalan]

See Borell-Cantelli lemma.

[gorgoiler]

I looked this up but I’m not sure I grasp your point.

Are you saying that:

- given a long string, we might ask “can this string be found in PI?”

- the probability of finding a long string in PI is infinitely small

- the number of possible strings in PI is infinitely large

- it’s not possible to decide if the answer is yes or no?

[rezeroed]

If a tree falls in the forest and no one is around to hear it fall. Or a modern take, if a disease has no symptoms is it really a disease.