Divergence
Also named here as harmonic series — the same set of essays touches all of them, so they are one junction rather than several.
A sum whose terms vanish and whose total does not
Add a half, a third, a quarter, and keep going. The terms shrink to nothing and the total passes every number there is — but so slowly that no computation will ever watch it happen.
The same terms, in a different order, adding to whatever is asked
Flip alternate signs in the harmonic series and it converges. Reorder the terms — add nothing, remove nothing — and it converges to any number chosen in advance. Addition stops being commutative, and the picture shows where it goes.
Named alongside it
The objects these essays reach for when they reach for this one.
ConvergenceHarmonic seriesLimitLogarithmAbsolute convergenceAlternating seriesBlock stackingCommutativityConditional convergenceThe Euler–Mascheroni constantOresmeRearrangement