User blog comment:Edwin Shade/Turing Machines and a Problem by Vel! Posed Half a Decade Ago/@comment-1605058-20171010173654/@comment-32876686-20171011050539

Okay then, I will just redefine the cardinals used so that they conform to my interpretation of them.

There are two questions I have though. Assuming $$\aleph_1$$ is in fact equal to the cardinality of the set of real numbers, then what would $$\aleph_2$$ be equal to number-wise ? That is, if you can correspond these infinities with types of numbers, then what number set comes after the real numbers in size ?

Also, does it makes sense to have an expression such as $$\aleph_\omega$$ or even $$\aleph_{\aleph_{\aleph_{\aleph_{._{._.}}}}}$$, where there is $$\omega$$ $$\aleph$$'s with a $$\aleph_0$$ on the very bottom ?