# When is a complex subsequence convergent?

In the complex set of numbers, what sequences have at least one convergent subsequence?

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What do you mean by "complex set"? Do you mean a set of complex numbers? Or is it actually the set rather than the numbers that you have in mind? –  Michael Hardy Oct 16 '11 at 16:48

As $\mathbb{C}$ is just $\mathbb{R}^2$ with additional structure (namely complex multiplication), the answer is provided by the Bolzanon-Weierstrass theorem.