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/Iksfen]

Since pi infinite digit expantion it contains every finite string of digits.

That is not true in principle. For example a number 0.101001000100001000001... (each time the string of 0s is one longer) has infinite expansion, but it does not contain finite string 2. Pi is also not proven to contain each finite string of digits. It is only strongly suspected.

Let's define mi = 0.123356789101112131415... (each finite string of digits written one after the other). Most infinite strings of digits will not appear in it. For example "11111111..." will not appear since no matter how far you go there will be a finite string at some point that will contain another digit

[u/jsundqui → u/Iksfen]

I think they said every finite string, not infinite