Can infinity contain infinity

[u/Loose-Balance3225]

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

[u/Mishtle]

If pi has no end it has to have every combination of numbers

This isn't true. Such a number is called "normal". Most non-repeating numbers are normal and pi is believed to be one of them. It's not been proven to be one though.

The number 0.1010010001... never repeats but only contains 0s and 1s.

but could it hold an infinite combination? Like 1 2 3 4... To infinity

Any sequence has what are called subsequences. Ignoring any number of items from the original sequence gives a new sequence.

Using the non-repeating number above, both the numbers 0.111... and 0.000..., along with many others, could be made from a subsequence of its digits.

If a number is normal, then it would contain every infinite sequence as a subsequence in this way. You might need to wait arbitrarily long for each next element to appear though.

[u/Bills_afterMATH → u/Mishtle]

Not correct. A number for which every block of digits appear is called either rich or disjunctive. Not normal. Of course all normal numbers are rich. Normality is a significantly stronger and more complicated condition than richness.