Matpic
mathematics, in pictures
Concept

Constructive proof

An argument that establishes something exists by exhibiting one, rather than by ruling out its absence.

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

U¬UU ∪ ¬U¬¬UU is an interval with 1 point taken out; ¬U is the inside of what is leftU and ¬U together miss the endpoints, and ¬¬U hands them back — so U ∨ ¬U is not everything and ¬¬U is not U

The middle that is not excluded

Either it is raining or it is not. Drop that as an axiom and what is left is still a logic — one with models made of open sets and of stages of knowledge, in which a set and its negation between them miss the boundary.

logic · non classical logic a matching that is not stableA1B2C3D4why that pair blocksD13would rather4has now23ADwould ratherChas nowBhow many of the 24 matchings have each number of blocking pairs40315283241516blocking pairsevery matching, sorted — the 4 stable ones first000011122222333333334456A1 B2 C3 D4 has 1 blocking pair: D and 3 would each rather have the otherall 24 matchings were formed and each put all 16 blocking questions; 4 of them came back with nonethe strip holds one cell per matching, sorted by that count with the 4 zeroes at the left

Nobody has a reason to run away

A matching is stable when no two people on opposite sides would both rather have each other than what they have — a condition that names nothing to build and everything to rule out. The surprise is that something always satisfies it, however perverse the rankings are made.

applied · stable matching

Named alongside it

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

BijectionBlocking pairCounterexampleDeferred acceptanceDouble negationExcluded middleExistence proofHeyting algebraIntuitionistic logicKripke modelOpen setPreference profile

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