Nombre réelEn mathématiques, un nombre réel est un nombre qui peut être représenté par une partie entière et une liste finie ou infinie de décimales. Cette définition s'applique donc aux nombres rationnels, dont les décimales se répètent de façon périodique à partir d'un certain rang, mais aussi à d'autres nombres dits irrationnels, tels que la racine carrée de 2, π et e.
Greatest element and least elementIn mathematics, especially in order theory, the greatest element of a subset of a partially ordered set (poset) is an element of that is greater than every other element of . The term least element is defined dually, that is, it is an element of that is smaller than every other element of Let be a preordered set and let An element is said to be if and if it also satisfies: for all By switching the side of the relation that is on in the above definition, the definition of a least element of is obtained.
Linearly ordered groupIn mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant. This may have different meanings. We say that (G, ≤) is a: left-ordered group if ≤ is left-invariant, that is a ≤ b implies ca ≤ cb for all a, b, c in G, right-ordered group if ≤ is right-invariant, that is a ≤ b implies ac ≤ bc for all a, b, c in G, bi-ordered group if ≤ is bi-invariant, that is it is both left- and right-invariant.
Connected relationIn mathematics, a relation on a set is called connected or complete or total if it relates (or "compares") all pairs of elements of the set in one direction or the other while it is called strongly connected if it relates pairs of elements. As described in the terminology section below, the terminology for these properties is not uniform. This notion of "total" should not be confused with that of a total relation in the sense that for all there is a so that (see serial relation).
