How to pronounce “uncountable set” in English

in a way that was so compelling. He exhibited two different infinite sets and proved that they're not equinumerous; they can't be put into one-to-onecorrespondence. It's traditional to talk about the uncountability of the real numbers. Cantor's big result was that the set of all real numbers is an uncountable set. Maybe if we'regoing to talk about countable sets, then I would suggest that we talk about Hilbert's Hotel, which really makes that idea perfectly clear.