The difference between Continuum and Countably infinite
Continuum is also noun with the meaning: a continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.
Countably infinite is also adjective with the meaning: that is both countable and infinite.
check bellow for the other definitions of Continuum and Countably infinite
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Continuum as a noun:
A continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.
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Continuum as a noun:
A continuous extent.
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Continuum as a noun (mathematics):
The set of real numbers; more generally, any compact connected metric space.
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Continuum as a noun (musical instruments):
A touch-sensitive strip, similar to an electronic standard musical keyboard, except that the note steps are of a semitone, and so are not separately marked.
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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.