
Infinite series explained - babuskov
https://www.youtube.com/watch?v=-EtHF5ND3_s
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dexwiz
I 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.

