Matpic
mathematics, in pictures
Concept

Uniformity

Convergence at a rate that works everywhere at once, rather than separately at each point.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

ji123456123456∀i ∃j : trueevery row carries at least one mark∃j ∀i : falsesome one column is marked all the way downthe relation "j is one more than i, counting round", on 6 rows and 6 columnsevery row has a mark: yes · some column is all marks: no

Every row, or one column

For every person there is someone who loves them, and there is someone who loves everyone, are the same six words in a different order. Draw the relation as a grid and they become two obviously different questions — one about rows, one about columns.

logic · quantifiers 1 steplength 2.00gap 0.7072 stepslength 2.00gap 0.2584 stepslength 2.00gap 0.14316 stepslength 2.00gap 0.035every staircase is exactly 2 long; a quarter circle is 1.5708 longthe finest one here is never more than 0.035 away from the curve, and it is still 2 long

The staircase that is not the diagonal

A staircase can be made to follow a quarter circle as closely as anyone likes. Its length is 2 at every stage and the arc's length is 1.5708, and no amount of refinement closes the gap — which is a fact about length rather than about staircases.

analysis · arc length

Named alongside it

The objects these essays reach for when they reach for this one.

CounterexampleApproximationArc lengthContinuityConvergenceDerivativeGibbs' phenomenonLimitNegationPredicate logicQuantifierQuantifier order

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