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Consider an infinite set [itex]X[/itex] with the

**finite complement topology**. I want to show that any infinite subset [itex]A[/itex] of [itex]X[/itex] is dense in [itex]X[/itex].

Now, I can show that every point of [itex]X[/itex] is a limit point of [itex]A[/itex].

Can this help me in any way to show that [itex]A[/itex] is dense in [itex]X[/itex]. Or could someone provide me with an alternative method.

By the way, my understanding of dense is that a subset of a set is dense if its closure coincides with the set.