[ChainOfFools]

> This means that there is no convergence because dividing left of zero, and right of zero, leads to different result.

Isn't this related to the reason why if a series can be proven to converge absolutely it's considered convergent? And the simpler tests like comparison, limit comparison, integral test for absolute value by just forcing the expression to be absolute notation?

I always just chalk this up to resolving an ambiguous meaning of "less than", in one sense referring to a relative X position from another spot A on the number line, and another sense referring to a relative X position from zero in either direction.