Ripheus23

For most of my relevant life, I have believed the Continuum Hypothesis on the ground that since Cantor proved the distinction between aleph-zero and aleph-zero+n, by referring to the distinction between the cardinality of the repeating vs. the nonrepeating infinite decimal numbers (in the diagonal argument, explicitly/implicitly/w/e), this indicated that our semiotic intuition of the continuum was the immediate alternate for the prior system-set, in which event it would "seem" as if aleph-C = aleph-one.

However, what if the answer is instead that aleph-C = aleph-aleph-zero? I.e. an aleph with a littler aleph with a zero, subscriptwise. This would be intuitive in the sense of being a "successor" set, of aleph-zero, immediately as it were. And indeed, if you compare the difference between "summing up" the first list of aleph-numbers, and the identification of aleph-aleph-zero (as the first of the second list), it seems (to me) that this is an image of the procedure of the continuum itself, i.e. the infinity of infinities on the first list sums to the continuum under aleph-aleph-zero.

This also would mean, though, that 2 to the power of aleph-zero, does not = aleph-1, but equals aleph-aleph-zero, which seems to indicate that 3 to the power of aleph-zero, would be aleph-aleph-aleph-zero, a number Cantor is reported to have believed to exist. {... and so on and on...}