Talk:The Inaccessible Cardinal/@comment-33102557-20190426193323/@comment-43912911-20200114173336

you can powerset any infinite cardinal (it can be aleph0, aleph1, alephω, aleph ω^ω^ω^ω... or any other infinite cardinal)  any amount of time  and it will lead you to bigger and bigger infinities.

The innaccessible cardinal is the cardinal you will never reach by doing that (even if you do it infinitely many times).

The conceptual jump beetween 0 and aleph0 and the conceptual jump beetween aleph0 and the innaccesible cardinal are the same because you will never reach aleph 0 by just exponentiating or superexponentiating or factorizing or [any other normal arithmetic function] a finite number. You will never reach any infinite sum with finite numbers using finite functions.

P.S. : sorry for the bad english