Correct me if I'm wrong, but

is regarded as the cardinality of the integers. It's the "first rung" of the infinities. The continuum hypothesis would claim that

That is, taking the power set of an infinite set means you exponentiate the cardinality of the original set in order to get the cardinality of the power set. (This always works for finite sets - it's only the infinite set we're talking about here.)

I'm not exactly sure what your F is, but if it corresponds to the cardinality of the power set of the reals, then the continuum hypothesis (which has not been proven) would say that

The wiki on El Aleph says that the aleph numbers and infinite sets "are related" to El Aleph. It seems to me, though, that the author was more interested in Jewish themes, and incorporated those more than the mathematical side of things, especially since, apparently, he wrote more than one story connected with Judaism.