In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation...

Look up total in Wiktionary, the free dictionary. Total may refer to: Total, the summation of a set of numbers Total order, a partial order without incomparable...

generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences...

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential...

In mathematics, an order topology is a specific topology that can be defined on any totally ordered set. It is a natural generalization of the topology...

partial cyclic order is a ternary relation that generalizes a (total) cyclic order in the same way that a partial order generalizes a total order. It is cyclic...

other. Partial orders thus generalize total orders, in which every pair is comparable. Formally, a partial order is a homogeneous binary relation that...

Teetotalism is the practice or promotion of total personal abstinence from the consumption of alcohol, specifically in alcoholic drinks. A person who...

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...

first when two actions are processed. By contrast, total-order planning maintains a total ordering between all actions at every stage of planning. Given...

Join and meet – Concept in order theory Map of lattices – Concept in mathematics Orthocomplemented lattice Total order – Order whose elements are all comparable...

method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items...

strict partial order that is connected is a strict total order. A relation is a total order if and only if it is both a partial order and strongly connected...

antisymmetric, asymmetric, transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder (weak order), or an equivalence relation...

or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus,...

In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism...

In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given...

and b in P, we have that: a ≤ b or b ≤ a. A partial order with this property is called a total order. These orders can also be called linear orders or chains...

Partial order – preorder that is antisymmetric Equivalence relation – preorder that is symmetric Total preorder – preorder that is total Total order – preorder...

every nonzero real number a. The total order is denoted a < b . {\displaystyle a<b.} being that it is a total order means two properties: given two real...

Total: From Joy Division to New Order is a compilation album of material from the British bands Joy Division and New Order. It was released in the United...

connected in an overall implicate order: I propose that each moment of time is a projection from the total implicate order. The term projection is a particularly...

well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every...

all terms sum to the total variance of the model output. A direct variance-based measure of sensitivity Si, called the "first-order sensitivity index",...

In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion...

the sorting to be unique, these two are restricted to a total order and a strict total order, respectively. Sorting n-tuples (depending on context also...

partial order is a total order that is compatible with it, in the sense that, if x ≤ y in the partial order, then x ≤ y in the total order as well. One can...

In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Basic examples...

quasi-order. Classically this defines a strict total order – indeed strict total order and total order can there be defined in terms of one another. Recall...