title: Order (mathematics)
text: # Order (mathematics)
  
  Order in mathematics may refer to:
  
  ## Set theory
  
  * 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
  
  * 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
  
  * 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
  
  * Multiplicative order in modular arithmetic
  * Order of operations
  * Orders of magnitude, a class of scale or magnitude of any amount
  
  ## Combinatorics
  
  * 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
  
  * 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
  
  * Long-range aperiodic order, in pinwheel tiling, for instance
  
  ## Graphs
  
  * 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
  
  In logic, model theory and type theory:
  
  * Zeroth-order logic
  * First-order logic
  * Second-order logic
  * Higher-order logic
  
  ## Order theory
  
  * 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
  
  * 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
  