Alternating series
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
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.
Nobody gets their own hat
Hand back a pile of hats at random and ask for the chance that not one person gets their own. The answer barely moves as the crowd grows — it is a third and a bit at four people, and a third and a bit at four thousand.
Named alongside it
The objects these essays reach for when they reach for this one.
Absolute convergenceApproximationCommutativityComplementary countingConditional convergenceConvergenceCounting argumentCounting two waysDerangementDivergencee, the numberHarmonic series