The difference between Countably infinite and Finite
When used as adjectives, countably infinite means that is both countable and infinite, whereas finite means having an end or limit.
check bellow for the other definitions of Countably infinite and Finite
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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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Finite as an adjective (of a quantity):
Having an end or limit; constrained by bounds; whose number of elements is a natural number.
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Finite as an adjective (grammar, as opposed to [[infinite]]):
limited by person or number.
Examples:
"The "goes" in "he goes" is a finite form of a verb"