Order (mathematics)

For order in other disciplines, see Order (disambiguation).

Order in mathematics may refer to:

## Set theory

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* Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionary
* Ordered set
* Order in Ramsey theory, uniform structures in consequence to critical set cardinality

## Algebra

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* Order (group theory), the cardinality of a group or period of an element
* Order of a polynomial (disambiguation)
* Order of a square matrix, its dimension
* Order (ring theory), an algebraic structure
* Ordered group
* Ordered field

## Analysis

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* Order (differential equation) or order of highest derivative, of a differential equation
* Leading-order terms
* NURBS order, a number one greater than the degree of the polynomial representation of a non-uniform rational B-spline
* Order of convergence, a measurement of convergence
* Order of derivation
* Order of an entire function
* Order of a power series, the lowest degree of its terms
* Ordered list, a sequence or tuple
* Orders of approximation in Big O notation
* Z-order (curve), a space-filling curve

## Arithmetic

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* Multiplicative order in modular arithmetic
* Order of operations
* Orders of magnitude, a class of scale or magnitude of any amount

## Combinatorics

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* Order in the Josephus permutation
* Ordered selections and partitions of the twelvefold way in combinatorics
* Ordered set, a bijection, cyclic order, or permutation
* Weak order of permutations

## Fractals

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* Complexor, or complex order in fractals
* Order of extension in Lakes of Wada
* Order of fractal dimension (Rényi dimensions)
* Orders of construction in the Pythagoras tree

## Geometry

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* Long-range aperiodic order, in pinwheel tiling, for instance

## Graphs

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* Graph order, the number of nodes in a graph
* First order and second order logic of graphs
* Topological ordering of directed acyclic graphs
* Degeneracy ordering of undirected graphs
* Elimination ordering of chordal graphs
* Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)

## Logic

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In logic, model theory and type theory:

* Zeroth-order logic
* First-order logic
* Second-order logic
* Higher-order logic

## Order theory

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* Order (journal), an academic journal on order theory
* Dense order, a total order wherein between any unequal pair of elements there is always an intervening element in the order
* Glossary of order theory
* Lexicographical order, an ordering method on sequences analogous to alphabetical order on words
* List of order topics, list of order theory topics
* Order theory, study of various binary relations known as orders
* Order topology, a topology of total order for totally ordered sets
* Ordinal numbers, numbers assigned to sets based on their set-theoretic order
* Partial order, often called just "order" in order theory texts, a transitive antisymmetric relation
* Total order, a partial order that is also total, in that either the relation or its inverse holds between any unequal elements

## Statistics

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* Order statistics
* First-order statistics, e.g., arithmetic mean, median, quantiles
* Second-order statistics, e.g., correlation, power spectrum, variance
* Higher-order statistics, e.g., bispectrum, kurtosis, skewness

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