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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
countable
countably many
uncountable
A term describing a set which is isomorphic
to a subet of the natural numbers. A countable set has
"countably many" elements. If the isomorphism is stated
explicitly then the set is called "a counted set" or "an
enumeration".
Examples of countable sets are any finite set, the {natural
numbers}, integers, and rational numbers. The {real
numbers} and complex numbers are not [proof?].
(1999-08-29)