Kevin Ullmann
Sep 3, 2018 · 1 min read

Great question. The set of cardinal numbers is at least countably infinite, but may be larger. You can always make a strictly larger set by taking the power set (set of all subsets). For example the cardinality of the reals is equal to the cardinality of the power set of the integers. So you can start from the integers and keep taking power sets to produce a countable sequence of aleph numbers. The set of all cardinalities may be uncountably infinite, though. I think the answer depends on whether you use the axiom of choice, but at this point I’m out of my depth! https://en.wikipedia.org/wiki/Cardinal_number

    Kevin Ullmann

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    Average level nerd that wishes he were actually an even bigger nerd.