Countable languages in TOC

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the set of all languages is uncountable, you can proof this using diagonalization method.

rest all are countable.

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What does countable infinite mean? If they are countable then how can they be infinite?

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a set is called countably infinite, if we can have one-one correspondence b/w element of a set and a natural numbers.

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always use cantor's theorem for this type of question