Zermelo and Cantor did. They concluded there were countably many, which turned out to be equivalent to the Axiom of Choice.
This isn’t right—aleph numbers are indexed by all ordinals, not just natural numbers. What’s equivalent to AC is that the aleph numbers cover all infinite cardinals.
Zermelo and Cantor did. They concluded there were countably many, which turned out to be equivalent to the Axiom of Choice.
This isn’t right—aleph numbers are indexed by all ordinals, not just natural numbers. What’s equivalent to AC is that the aleph numbers cover all infinite cardinals.