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A set equipped with a total order is a totally ordered set; the terms simply ordered set, linearly ordered set, and loset are also used. The term chain is sometimes defined as a synonym of totally ordered set , [5] but refers generally to some sort of totally ordered subsets of a given partially ordered set.
t. e. In mathematics, an algebraic number field (or simply number field) is an extension field of the field of rational numbers such that the field extension has finite degree (and hence is an algebraic field extension). Thus is a field that contains and has finite dimension when considered as a vector space over .
Totally bounded space. In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily closed. A totally bounded set can be covered by finitely many subsets of every fixed “size” (where the meaning of “size” depends on the structure of the ambient ...
Totally disconnected space. In topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets. In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only ...
A function is (totally) differentiable if its total derivative exists at every point in its domain. Conceptually, the definition of the total derivative expresses the idea that d f a {\displaystyle df_{a}} is the best linear approximation to f {\displaystyle f} at the point a {\displaystyle a} .
Bounded set. An artist's impression of a bounded set (top) and of an unbounded set (bottom). The set at the bottom continues forever towards the right. In mathematical analysis and related areas of mathematics, a set is called bounded if all of its points are within a certain distance of each other. Conversely, a set which is not bounded is ...
In 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 ...
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [1] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.
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