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HOW IT WORKS
Order (mathematics)
Summary
Order
in mathematics may refer to:
Set theory
edit
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
edit
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
edit
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
edit
Multiplicative order
in modular arithmetic
Order of operations
Orders of magnitude
, a class of scale or magnitude of any amount
Combinatorics
edit
Order in the
Josephus permutation
Ordered selections and partitions
of the twelvefold way in combinatorics
Ordered set, a
bijection
,
cyclic order
, or
permutation
Unordered
subset
or combination
Weak order of permutations
Fractals
edit
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
edit
Long-range aperiodic order, in
pinwheel tiling
, for instance
Graphs
edit
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
edit
In logic, model theory and type theory:
Zeroth-order logic
First-order logic
Second-order logic
Higher-order logic
Order theory
edit
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
edit
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