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Infinite series explained
- dexwiz 10y agoI always feel like there is some sort of `cheating` or `hacking` going on with infinite series. It's abusing a continuous or infinite concept by representing it with a discrete concept. Then going, "Wow it breaks!" Of course it breaks. Yes, there are an infinite number of terms you can rearrange to converge around ln(2), or 1/2 ln(2), or pi, but you are always going to have some unmatched terms. Also if you were to write the expression describing the two orderings, they would have to be different to produce a different order. Also commutativity does not make sense to me if one side of the expression is unbounded. Mathematicians seem to like to muck around with the first part of a series, and then claim it all works out since its unbounded. That seems analogous to changing a circle's diameter, and then claiming it does not matter since it's still round. Maybe if they were more clear that the ordering is what's key here, not the total.