Discrete Math Can infinity contain infinity

If pi has no end it has to have every combination of numbers but could it hold an infinite combination? Like 1 2 3 4... To infinity

Please help this is missing my brain up

• Upvotes

65% Upvoted

•

u/mpaw976 May 06 '26

As stated, no, that's not guaranteed because there's a difference between having every finite string, and every infinite string.

As a simple example,

0.101101110111101111101...

Will contain every finite string of 1s, but it won't contain 111... repeating forever.

In fact, any given decimal number only "has room" to end in a single infinite string. E.g. it can't end in both all 0s and all 1s.

Isn't that neat?