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If I have a series of elements of a Banach space that converges unconditionally (it converges regardless of the order of the terms), why is it the case that the sum does not depend on the order of the terms?

I'm reading a text on bases in Banach spaces and it threw out "The sum does not depend on the permutation of the index set" as a remark, but I'm finding it more difficult than I expected to prove this (I'm a beginner at this sort of thing).

Thanks

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    If you've answered your own question, you can post an answer (a hint or a full answer, as you see fit) and accept it so that the question doesn't remained as an unanswered question in the system.2012-12-05

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