The difference between Countably infinite and Infinite
When used as adjectives, countably infinite means that is both countable and infinite, whereas infinite means indefinably large, countlessly great.
Infinite is also numeral with the meaning: infinitely many.
check bellow for the other definitions of Countably infinite and Infinite
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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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Infinite as an adjective:
Indefinably large, countlessly great; immense.
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Infinite as an adjective:
Boundless, endless, without end or limits; innumerable.
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Infinite as an adjective:
With plural noun: infinitely many.
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Infinite as an adjective (mathematics):
Greater than any positive quantity or magnitude; limitless.
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Infinite as an adjective (set theory, of a set):
Having infinitely many elements.
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Infinite as an adjective (grammar):
Not limited by person or number.
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Infinite as an adjective (music):
Capable of endless repetition; said of certain forms of the canon, also called perpetual fugues, constructed so that their ends lead to their beginnings.
Examples:
"rfquotek Moore (Encyc. of Music)"