I mean from what i understand from the situation is the following:
- There are infinite Universes like: 1, 2, 3, 4, etc.
- Each of them has further infimite Universes like lets say Universe 1 from above is: 1.1, 1.2, 1.3, 1.4, etc
- Each of those Universes of Universe 1 contains further imfinite Universes like Universe 1.1 from above would have: 1.1.1, 1.1.2, 1.1.3, etc
- And so on.
Now lets list the base Universe and its expznsions:
U1: 1 → 1.1 → 1.1.1 → 1.1.1.1 → …
U2: 1 → 1.2 → 1.2.1 → 1.2.1.1 → …
U3: 2 → 2.1 → 2.1.1 → 2.1.1.1 → …
U4: 1 → 1.1 → 1.1.2 → 1.1.2.1 → …
....
adinfinitum.
Now take 1st step of U1: 1
Now take second step of U2: 2 (2 of 1.2)
Now take 3rd step of U3: 1 (1 of 2.1.1)
Adinfinitum.
We have (1, 2, 1, etc)
Now we just change those step numbers and get (2, 1, 2, etc)
Now listing it, we will get the Universe that differs from all the Universes at each particular step:
U*: 2 → 2.1 → 2.1.2 → etc
This new Universe differs from all the Universes listed before but still exist inside the multiverse OP described. So Cantor's diagonal theorem still seems applicable/to work unless i am missing smth.