transitive (idea) by Evandar

A set A is said to be transitive if whenever x is in A and y is in x then y is in A. In other words, every member of A is a subset of A.

The axiom of foundation implies that any transitive set must contain the empty set.

Examples of useful transitive sets are:

Every natural number is transitive
More generally, every ordinal (and therefore every cardinal) is transitive
Each member V_a of the cumulative heirachy of sets (sets formed from the empty set by repeatededly taking power sets) is transitive

Transitive Verb	transitivity	Transitive closure	The Man Felt an Iron Hand Grasp Him by the Hair, at the Nape. Not One Hand, a Hundred Hands Seized Him, Each by the Hair, and Tore Him Head to Foot, the Way You Tear Up a Sheet of Paper, Into Hundreds of Little Pieces
Percolation	reflective	Nontransitive dice	syllogistic logic
Equivalence relation	Intransitive	reflexive	Japanese Verb Pairs
proof using coupling that the site percolation probability function is monotone	critical percolation	argument structure	unaccusative
Meronymy	actant	Extensional Mereology	v.i.
Vince McMahon's Gulp Of Fear	wolf tickets	Combinatorics	set theory