> Who says Michael is speaking of Aleph-null,

No one; it's a reasonable assumption from the stated operations. But
feel free to choose a higher cardinality.

> he did not mention that we
> were dealing with integers. Aleph-null is to me
> the quantity of all possible integers.

Pretty much; by Cantor's definition, it's the size of the set of all
natural numbers. But since "all integers", "all even integers", "all
natural numbers evenly divisible by 42", etc. all have the same
cardinality, the distinction is sans difference.

> In real number theory there are
> more reals than integers, so there are more projections on
> infinity.

Sure; as mentioned, pick whatever cardinality you like. I just picked
the one that is most commonly associated with the term "infinity".

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