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[Turing Machine Problem] A set S is countable if S is finite or there is a 1-1 function from N, the set of natural numbers onto S.
i. Prove that for any finite alphabet S, S* is countable.
ii. Show that any subset of a countable set is countable.
iii. As a corollary show that any decidable set is countable.
Hint: You can use the fact that a decidable set can be enumerated in increasing order.
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