Order (mathematics)
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Contents
For order in other disciplines, see Order.Order in mathematics may refer to:
In algebra
- Order (group theory), the cardinality of a group or period of an element
- Order, or degree of a polynomial
- Order, or dimension of a matrix
- Order (ring theory), an algebraic structure
- Ordered group
- Ordered field
In arithmetic
- Order (number theory), the multiplicative order in modular arithmetic
- Orders of magnitude, a class of scale or magnitude of any amount
- Order of operations
In analysis
- Orders of approximation in Big O notation
- Order of convergence, a measurement of convergence
- Order (differential equation), or order of highest derivative, of a differential equation
- Order of an entire function
- Ordered list, a tuple or sequence
- Z-order (curve), a space-filling curve
- NURBS order, a number one greater than the degree of the polynomial representation of a non-uniform rational B-spline
In combinatorics
- Order in the Josephus permutation
- Weak order of permutations
- Ordered selections and partitions of the twelvefold way in combinatorics
- Ordered set, a permutation, bijection or cyclic order
- Unordered subset or combination
In statistics
- Mean, median, quantiles are first-order statistics
- Variance, correlation, power spectrum are second-order statistics
- Skewness, bispectrum, kurtosis are examples of higher-order statistics
In fractals
- Complexor, or complex order in fractals
- Orders of construction in the Pythagoras tree
- Order of extension in Lakes of Wada
- Order of Rényi dimensions
In geometry
- Long-range aperiodic order, in pinwheel tiling for instance
In graphs
- Graph order, the number of nodes in a graph
- Ordered pair, including undirected and directed graphs
- Ordered triple, or mixed graph
Order theory
- Order theory, which studies various binary relations known as orders
- Order (journal), an academic journal on order theory
- 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
- Dense order, a total order where between any unequal pair of elements there is always an intervening element in the order
- Order topology, a topology of total order for totally ordered sets
- Ordinal numbers, which are assigned to sets based on their set-theoretic order
- Glossary of order theory
- List of order theory topics
In other mathematical theories
- Order in Ramsey theory, uniform structures in consequence to critical set cardinality
- Set theory (music) encompasses ordered pitch and pitch classes (Musical set theory)
- Type theory encompasses: zeroth-order, first-order, second-order and higher-order logic
Categories:- Mathematical terminology
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