It's worth mentioning the Infinity is an Aleph Zero.

I don't have near enough High Math mojo,

to describe what Aleph One is or why it's different

from Aleph Zero. Anyone trying to get that number

via the D&D rule set, is up against not just doing it,

but also explaining *what* it is.

Remains quite a cookie, for both Pun-pun lovers and haters.

Cantor's Diagonal Argument is the best explanation I've seen for the difference between countable(aleph zero) and uncountable(aleph one) infinities. Here's my take on it.

First, imagine an infinitely long sequence, where each element is either 1 or 0. One such sequence could be 111111..., another 000000..., another 10101010..., and so on. Now, imagine that we take all of these sequences, and arrange

*them* into a list. It might look something like this:

1: 111111111....

2: 000000000....

3: 101010101....

4: 010101010....

5: 100100100....

6: 011011011....

...

Thus, we associate each natural number with one such possible sequence. Now, one might think that, since there are infinitely many natural numbers, once we had associated every natural number with a sequence, there would be no more sequences. One would be wrong. Consider the sequence

*S*, defined thus: the nth element in

*S* is 0 if the nth element of the nth sequence is 1, and 1 otherwise. This sequence is clearly not anywhere in the list - it is by its very nature different from every sequence in the list. We can append this specific sequence to the list, but from the same definition, another sequence will arise which does not fit in the list. As long as every sequence on the list can be associated with a natural number, there will be sequences not on the list. Therefore, the set which contains all the possible sequences must have a larger cardinality than the set of all natural numbers, or, in layman's terms, there must be more possible sequences than natural numbers.