## Please explain how Conditionally Convergent can be valid? [closed]

I understand the basic idea of Conditionally Convergent (some infinitely long series can be made to converge to any value by reordering the series). I just do not understand how this could possibly be true. I think it defies common sense and seems like a clear violation of the Commutative Law.

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This question would be more appropriate for math.stackexchange.com or the other sites listed in the FAQ. MO is for research-level questions. – Ben Webster Dec 16 2010 at 19:00
OK. Done: math.stackexchange.com/questions/14560/… – Toby Dec 16 2010 at 19:12
Toby, if you're still reading this: The commutative law applies to sums of <b>finitely many</b> numbers. – Michael Hardy Dec 17 2010 at 0:52