The difference between Countably infinite and Denumerable
When used as adjectives, countably infinite means that is both countable and infinite, whereas denumerable means 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 Countably infinite and Denumerable
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Countably infinite as an adjective (set theory, of a set):
That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.
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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."