## 5 comments on “Infinite Series – A Health and Safety Warning”

1. It seems that with such alternating “convergent series,” we can separate all the positive and negative terms into two divergent series leaving us with, you should pardon, infinity – infinity = ?, in short, anything we like. In a sense, this really returns us–past the gymnastics–to the Great Crisis introduced by Weierstrass in 1872.

Now combine the history of Hilbert’s “On The Infinite,” Godel’s Incompleteness Thm., and finally the birth of algorithmic information theory–and finally add General Relativity and Quantum Mechanics (intuited by Hilbert to an extent in “On the Infinite”), and voila–you can construct a convergent infinite series approximately modeling a finite interrelationship in physical reality.

That is, this math is the drawing of a finite algorithmic information target bullseye about the intersection of the previously shot arrow and the tree. However, if there is a law of physics–an empirical pattern in our sensory perception (what axioms really are, per Bertram Russell and Kurt Godel) to how arrows tend to hit a tree, such infinite series constructs can be a useful minimal shorthand to describe it.

2. When you take the limit of the rearranged series, you are essentially making a different series. You cop out by saying that at infinity, you include everything, but that really isn’t the case, or your limits would be the same.

Yeah, you can argue around me by defining your terms and qualifying your logic, but if you subscribe to the view that there are larger and smaller infinities, your conclusion is faulty. Your modified series excludes some terms ad infinitum, so of course its limit is different.