Basic concepts in set theory

2 artículos

Ahlswede khachatrian theorem Algebra Algebra of past Almost disjoint sets Bijection Bijection injection and surjection Block design Carroll diagram Choice function Cocountability Codomain Cofiniteness Combinatorial design Complement Content Cover Covering design Delta ring Domain Dynkin system Erd's ko rado theorem Extremal problems for finite sets Family of sets Fiber Finite character Fisher inequality Function Function composition Generalized quadrangle Greedoid Growth function Helly family Hellys theorem History of the function concept Horizontal line test Hypergraph Identity function Incidence structure Inclusion map Indexed family Indicator vector Injective function Intersection Inverse function Jouanolous trick K cell Kirkmans schoolgirl problem Kruskal katona theorem Laminar set family Large set Levi graph Limitation of size Locally discrete collection Locally finite collection Lubell yamamoto meshalkin inequality Map Matroid Maximum coverage problem Monotone class theorem Monotone dualization Near polygon Noncrossing partition Partition regularity Pi system Point finite collection Polar space Predictable algebra Product algebra Property b Radons theorem Randolph diagram Range Ring of set Saturated set Sauer shelah lemma Separable algebra Set cover problem Set function Set theoretic definition of natural numbers Shapley folkman lemma Sigma ideal Sigma ring Smooth maximum Social golfer problem Sperner family Sperners theorem Steiner system Surjective function Transversal Tverbergs theorem Two graph Union closed sets conjecture

Recreational, History & Meta BachilleratoExplicación10 min

Three Switches, One Visit, and the State Light Cannot Carry

Six pairings have to be separated by a single observation, and a light-only strategy always leaves at least two candidates standing. Warmth is a genuine third readable state, and three states handed to three bulbs give exactly six readings, one per pairing. The article carries the impossibility count and the four-switch case where the trick fails.

Recreational, History & Meta BachilleratoExplicación9 min

Ten Bags, One Reading: 55 Coins Turn the Dial Into a Label

Taking one coin from each bag reads 9.9 ounces whichever bag is light, and the failure is blindness rather than imprecision. Loading i coins from bag i makes the dial an injective function of the culprit, at a cost of the tenth triangular number. A 45-coin variant is cheaper, and powers of two identify any subset of light bags from one reading.