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Show that the following property holds for countable sets: if S_1, S_2,S_3,... is a sequence of...

Show that the following property holds for countable sets:

if S_1, S_2,S_3,... is a sequence of countable sets of real numbers, then the set S formed by taking all the elements that belong to at least one of the sets S_i is also a countable set.

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