inductively ordered

A partially ordered setMathworldPlanetmath A is inductively ordered iff every chain of elements of A has an upper bound in A.

Examples. ‚ÄČThe power setMathworldPlanetmath 2M of any set M is inductively ordered by the set inclusion (; any finite setMathworldPlanetmath of integers is inductively ordered by divisibility.

Cf. inductive setMathworldPlanetmath.

Title inductively ordered
Canonical name InductivelyOrdered
Date of creation 2013-03-22 14:55:21
Last modified on 2013-03-22 14:55:21
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 8
Author rspuzio (6075)
Entry type Definition
Classification msc 06A99
Related topic ZornsLemma
Defines inductive order
Defines inductively orderes set