In mathematics, a binary relation R is said to be dense if, for all R-related x and y, there is a z such that x and z and also z and y are R-related.
Formally:
For example, a strict partial order < is a dense order iff < is a dense relation.
Every reflexive relation is dense.
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Dense order — In mathematics, a partial order ≤ on a set X is said to be dense if, for all x and y in X for which x < y, there is a z in X such that x < z < y. The rational numbers with the ordinary ordering are a densely ordered set in this sense, as … Wikipedia
dense — [dens] adj [Date: 1400 1500; : Latin; Origin: densus] 1.) made of or containing a lot of things or people that are very close together = ↑thick dense undergrowth/forest/woodland/jungle etc ▪ A narrow track wound steeply up through dense forest. ▪ … Dictionary of contemporary English
dense — [ dens ] adjective * ▸ 1 with close things/people ▸ 2 smoke/gas: thick ▸ 3 person: stupid ▸ 4 not easy to understand ▸ 5 substance: heavy 1. ) with a lot of trees, plants, or leaves growing close together: dense undergrowth a ) containing a lot… … Usage of the words and phrases in modern English
Dense submodule — In abstract algebra, specifically in module theory, a dense submodule of a module is a refinement of the notion of an essential submodule. If N is a dense submodule of M, it may also be said it may alternatively be said that N ⊆ M is a… … Wikipedia
dense — [[t]de̱ns[/t]] denser, densest 1) ADJ GRADED Something that is dense contains a lot of things or people in a small area. Where Bucharest now stands, there once was a large, dense forest... Its fur is short, dense and silky... They went out on to… … English dictionary
dense */ — UK [dens] / US adjective Word forms dense : adjective dense comparative denser superlative densest 1) a) with a lot of trees, plants, or leaves growing close together dense woodland b) containing a lot of things or people close together a dense… … English dictionary
dense — adjective 1 CLOSE TOGETHER made of several things that are closely packed together: He forced his way through the dense crowd. | Dense jungle covered the whole area. 2 SMOKE/MIST difficult to see through or breathe in: dense fog | a dense black… … Longman dictionary of contemporary English
dense — [dens] adj 1) consisting of a lot of things, people, trees etc that are all very close together a dense crowd/forest[/ex] 2) thick and difficult to see through dense smoke/cloud/fog[/ex] 3) science a dense substance is very heavy in relation to… … Dictionary for writing and speaking English
Clausius–Mossotti relation — The Clausius–Mossotti relation is named after the Italian physicist Ottaviano Fabrizio Mossotti, whose 1850 book[1] analyzed the relationship between the dielectric constants of two different media, and the German physicist Rudolf Clausius, who… … Wikipedia
Ordre dense — Sommaire 1 Ensemble ordonné dense en lui même 2 Sous ensemble dense d un ensemble ordonné 2.1 Définition 2.2 Lien avec la topologie … Wikipédia en Français
