uncountability
Noun
Meaning
uncountability (countable and uncountable, plural uncountabilities)
(countable, uncountable) The quality of being uncountable.
the grammatical uncountability of a noun
the uncountability of the stars in the night sky
Antonym: countability
Examples
Cantor gave two proofs that the cardinality of the set of integers is strictly smaller than that of the set of real numbers (see Cantor's first uncountability proof and Cantor's diagonal argument ).
So it is not obvious which one is the appropriate generalization of "uncountability" when the axiom fails.