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