The difference between Countable and Countably infinite
When used as adjectives, countable means capable of being counted, whereas countably infinite means that is both countable and infinite.
check bellow for the other definitions of Countable and Countably infinite
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Countable as an adjective:
Capable of being counted; having a quantity.
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Countable as an adjective (mathematics, of a set):
Finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.
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Countable as an adjective (mathematics, of a set):
Countably infinite; having a bijection with the natural numbers.
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Countable as an adjective (grammar, of a noun):
Freely usable with the indefinite article and with numbers, and therefore having a plural form.
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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.