The difference between Countable set and Denumerable
Countable set is also noun with the meaning: a set that is countable.
Denumerable is also adjective with the meaning: capable of being assigned a bijection to the natural numbers. applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.
check bellow for the other definitions of Countable set and Denumerable
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Countable set as a noun (set theory):
A set that is countable.
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Denumerable as an adjective (mathematics):
Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.
Examples:
"The empty set is not denumerable because it is finite; the rational numbers are, surprisingly, denumerable because every possible fraction can be assigned a natural number and vice versa."