The reasons for our failure were as uncountable as the grains of sand on a beach.
(mathematics) Incapable of being put into one-to-one correspondence with the natural numbers or any subset thereof.
Cantor’s “diagonal proof” shows that the set of real numbers is uncountable.
(grammar, of a noun) That cannot be used freely with numbers or the indefinite article, and therefore usually takes no plural form. Example: information.
Many languages do not distinguish countable nouns from uncountable nouns.
One meaning in law of the usually uncountable noun "information" is used in the plural and is countable.