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Set with exactly one element
In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly one element. For example, the set { 0 } {\displaystyle \{0\}}
Singleton_(mathematics)
Topics referred to by the same term
Singleton or singleton in Wiktionary, the free dictionary. Singleton may refer to: Singleton (mathematics), a set with exactly one element Singleton field
Singleton
Any one of the distinct objects that make up a set in set theory
{\displaystyle \ni } is a subset of P(U) × U. Identity element Singleton (mathematics) Weisstein, Eric W. "Element". mathworld.wolfram.com. Retrieved
Element_of_a_set
Programming technique to restrict a class to a single instance
the constructors of a class) The term comes from the mathematical concept of a singleton. Singletons are often preferred to global variables because they
Singleton_pattern
Logical quantifier
\exists !} . Essentially unique Extension by definition One-hot Singleton (mathematics) Uniqueness theorem Weisstein, Eric W. "Uniqueness Theorem". mathworld
Uniqueness_quantification
Collection of mathematical objects
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects:
Set_(mathematics)
Basic framework of mathematics
Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory
Foundations_of_mathematics
Set of all points in a function's domain that all map to some single given point
{\displaystyle y} under a function f {\displaystyle f} is the preimage of the singleton set { y } {\displaystyle \{y\}} , that is f − 1 ( y ) = { x : f ( x )
Fiber_(mathematics)
American businessman (1916–1999)
developing Teledyne. During his first two years at Annapolis, Singleton ranked first in mathematics out of a class of 820 students. A reoccurring medical problem
Henry_Earl_Singleton
A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol,
Mathematical_object
Association of one output to each input
not be a set. In usual mathematics, one avoids this kind of problem by specifying a domain, which means that one has many singleton functions. However, when
Function_(mathematics)
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly
Philosophy_of_mathematics
Peano Mathematical induction Structural induction Recursive definition Naive set theory Element (mathematics) Ur-element Singleton (mathematics) Simple
List of mathematical logic topics
List_of_mathematical_logic_topics
Upper bound in coding theory
In coding theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on
Singleton_bound
7-regular undirected graph with 50 nodes and 175 edges
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges. It is the unique
Hoffman–Singleton_graph
Finite ordered list of elements
called the empty tuple. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term "infinite tuple" is occasionally
Tuple
Branch of mathematics that studies sets
a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set
Set_theory
object-oriented programming, a singleton class has exactly one instance. In mathematics, a singleton is a set having exactly one element. In linguistics, a hapax legomenon
Glossary_of_computer_science
of S Lebesgue's decomposition theorem – Theorem in mathematical measure theory Singleton (mathematics) – Set with exactly one element Singular measure –
Discrete_measure
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Regular graph with girth more than twice its diameter
doi:10.1016/j.laa.2009.07.018. Singleton, Robert R. (1968), "There is no irregular Moore graph", American Mathematical Monthly, 75 (1): 42–43, doi:10
Moore_graph
Natural number
as a set that contains all numbers before it, 1 is represented as the singleton { 0 } {\displaystyle \{0\}} , a set containing only the element 0. The
1
Form of mathematical proof
Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that
Mathematical_induction
Overview of and topical guide to logic
Russell's paradox Sequence (mathematics) Set (mathematics) Set of all sets Simple theorems in the algebra of sets Singleton (mathematics) Skolem paradox Subset
Outline_of_logic
All numbers between two given numbers
In mathematics, an interval is the set of all real numbers lying between two fixed endpoints with no "gaps". For example, the set of real numbers consisting
Interval_(mathematics)
Symbolic description of a mathematical object
In mathematics, an expression is an arrangement of symbols following the context-dependent, syntactic conventions of mathematical notation. Symbols can
Expression_(mathematics)
Academic journal
Recreational Mathematics Magazine which ran during the years 1961 to 1964, was the editor for many years. Charles Ashbacher and Colin Singleton took over
Journal of Recreational Mathematics
Journal_of_Recreational_Mathematics
Symbol representing a mathematical object
In mathematics, a variable (from Latin variabilis 'changeable') is a symbol, typically a letter, that refers to an unspecified mathematical object. One
Variable_(mathematics)
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
Additional mathematical object
In mathematics, a structure on a set (or on some sets) refers to providing or endowing it (or them) with certain additional features (e.g. an operation
Mathematical_structure
Confederate Army officer, US Diplomat (1833–1916)
John Singleton Mosby (December 6, 1833 – May 30, 1916), also known by his nickname "Gray Ghost", was an American military officer who was a Confederate
John_S._Mosby
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Theorem for proving more complex theorems
In mathematics and other fields, a lemma (pl.: lemmas or lemmata) is a generally minor, proven proposition which is used to prove a larger statement.
Lemma_(mathematics)
Finding the largest graph of given diameter and degree
0497, MR 0140437 Singleton, Robert R. (1968), "There is no irregular Moore graph", American Mathematical Monthly, 75 (1), Mathematical Association of America:
Degree_diameter_problem
Mathematically obvious
members Trivial group: the mathematical group containing only the identity element Trivial ring: a ring defined on a singleton set "Trivial" can also be
Triviality_(mathematics)
Mathematical set containing no elements
In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic
Empty_set
Tool to track locally defined data attached to the open sets of a topological space
Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian
Sheaf_(mathematics)
American economist
Graduate School of Business, Singleton teaches a variety of degree courses in finance. Singleton received a BA in mathematics from Reed College in 1973,
Kenneth_Singleton
Generalization of vector spaces from fields to rings
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative)
Module_(mathematics)
Topological space that is maximally disconnected
topology and related branches of mathematics, a totally disconnected space is a topological space that has only singletons as connected subsets. In every
Totally_disconnected_space
Set of the values of a function
In mathematics, the image of a function f : X → Y {\displaystyle f:X\to Y} is the set of all f ( x ) {\displaystyle f(x)} such that x {\displaystyle
Image_(mathematics)
Infinite sum
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus
Series_(mathematics)
Limitative results in mathematical logic
published by Kurt Gödel in 1931, are important both in mathematical logic and in philosophy of mathematics. The theorems are interpreted as showing that Hilbert's
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Statement that is taken to be true
modern logic, an axiom is a premise or starting point for reasoning. In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom". Logical
Axiom
In mathematics, a statement that has been proven
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses
Theorem
Symbol representing a property or relation in logic
Equality (mathematics) § Axioms). Other properties can be derived from these, and they are sufficient for proving theorems in mathematics. Similarly
Predicate_(logic)
Collection of sets in mathematics that can be defined based on a property of its members
In set theory and its applications throughout mathematics, a class is a collection of mathematical objects (often sets) that can be unambiguously defined
Class_(set_theory)
All-encompassing set or class
In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a universe is a collection that contains
Universe_(mathematics)
Fields relating to the anti-de Sitter group
"Singleton physics". arXiv:hep-th/9901043. Dirac, P. A. M. (1963). "A Remarkable Representation of the 3 + 2 de Sitter Group". Journal of Mathematical
Singleton_field
Index of articles associated with the same name
Stratification has several usages in mathematics. In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing
Stratification_(mathematics)
Function, homomorphism, or morphism
In mathematics, a map or mapping is a function in its general sense.[vague] These terms may have originated as from the process of making a geographical
Map_(mathematics)
Technique invented by Paul Cohen for proving consistency and independence results
since served as a powerful technique, both in set theory and in areas of mathematical logic such as computability theory. Descriptive set theory uses the notions
Forcing_(mathematics)
Perkins B&W 17m January 2, 1951 Famous Men & Women of the World John Singleton Copley (Visual Images); David W. Powell & Cherill Anson color 7m 1974
List of Encyclopædia Britannica Films titles
List_of_Encyclopædia_Britannica_Films_titles
Mathematical construction of a set with an equivalence relation
In mathematics, a setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional
Setoid
Mathematical set formed from two given sets
In mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is an
Cartesian_product
English schoolmaster, soldier and cricketer (1913–2002)
was the England cricketer Betty Snowball, who taught mathematics and wicket-keeping. Singleton ran the school to a robust, rural routine: outdoor physical
Michael_Singleton
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Set whose elements all belong to another set
In mathematics, a set A is a subset of a set B if and only if all elements of A are also elements of B; B is then a superset of A. It is possible for
Subset
Mathematical concept for comparing objects
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments
Equivalence_relation
examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel
Implementation of mathematics in set theory
Implementation_of_mathematics_in_set_theory
Mathematician (1845–1918)
the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between
Georg_Cantor
Type of infinite structure
In mathematical logic, and more specifically in model theory, an infinite structure ( M , < , … ) {\displaystyle (M,<,\dots )} that is totally ordered
O-minimal_theory
Triangle of numbers
values count partitions of a set in which a given element is the largest singleton. It is named for its close connection to the Bell numbers, which may be
Bell_triangle
Diagram that shows all possible logical relations between a collection of sets
(April 2023). "The Venn Behind the Diagram". Mathematics Today. Vol. 59, no. 2. Institute of Mathematics and its Applications. pp. 53–55. Lewis, Clarence
Venn_diagram
American mathematician and computer scientist
Moore (November 23, 1925 – June 14, 2003) was an American professor of mathematics and computer science, the inventor of the Moore finite state machine
Edward_F._Moore
Sequence of words formed by specific rules
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
Formal_language
3-volume treatise on mathematics, 1910–1913
(often abbreviated PM) is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and
Principia_Mathematica
Concept in model theory
v t e Mathematical logic General Axiom list Cardinality First-order logic Formal proof Formal semantics Foundations of mathematics Information theory Lemma
Strength_(mathematical_logic)
Size of a possibly infinite set
In mathematics, a cardinal number, or cardinal for short, is a kind of number that measures the cardinality of a set, i.e., how many elements there are
Cardinal_number
Set of the elements not in a given subset
edu. Retrieved 2020-09-04. "Complement (set) Definition (Illustrated Mathematics Dictionary)". www.mathsisfun.com. Retrieved 2020-09-04. Halmos 1960,
Complement_(set_theory)
Number of arguments required by a function
In logic, mathematics, and computer science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics
Arity
Paradox in set theory
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician
Russell's_paradox
American astronomer (1846–1914)
Edward Singleton Holden (November 5, 1846 – March 16, 1914) was an American astronomer and the fifth president of the University of California. He was
Edward_S._Holden
Mathematical theory of data types
In mathematical logic, and theoretical computer science, type theory is the study of formal systems that classify expressions or mathematical objects by
Type_theory
British neurogeneticist
Andrew B. Singleton is a British neurogeneticist currently working in the USA. He was born in Guernsey, the Channel Islands in 1972, where he lived until
Andrew_Singleton
Hungarian and American mathematician and physicist (1903–1957)
many fields, including mathematics, physics, economics, computing, and statistics. He was a pioneer in building the mathematical framework of quantum physics
John_von_Neumann
A list of articles with mathematical proofs: Bertrand's postulate and a proof Estimation of covariance matrices Fermat's little theorem and some proofs
List_of_mathematical_proofs
One-to-one correspondence
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set
Bijection
Method of deriving conclusions
proof by contradiction, and mathematical induction. Mathematical logic, a subfield of mathematics and logic, uses mathematical methods and frameworks to
Rule_of_inference
Pair of mathematical objects
In mathematics, an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. If a and b are different, then (a,b) is different
Ordered_pair
Study of parts and the wholes they form
of his primitive singleton operator that, given the necessity (perceived by Lewis) of avoiding philosophically motivated mathematical revisionism, "I have
Mereology
Class of financial models with stochastic volatility and jumps
Stochastic Volatility Jump Models (SVJ models) are a class of mathematical models in quantitative finance that combine stochastic volatility dynamics with
Stochastic volatility jump models
Stochastic_volatility_jump_models
Standard system of axiomatic set theory
of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated
Zermelo–Fraenkel_set_theory
School of thought in philosophy of mathematics
philosophy of mathematics, logicism is a school of thought comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an
Logicism
Input to a mathematical function
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. For example
Argument_of_a_function
Target set of a mathematical function
In mathematics, a codomain or set of destination of a function is a set into which all of the outputs of the function are constrained to fall. It is the
Codomain
Mathematical logician and philosopher
foundations of mathematics), building on earlier work by Frege, Richard Dedekind, and Georg Cantor. Gödel's discoveries in the foundations of mathematics led to
Kurt_Gödel
Area of mathematical logic
In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing
Model_theory
Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Concept in graph theory
complement of the aforementioned line graph on GQ(2, 4). The Hoffman–Singleton graph is an srg(50, 7, 0, 1). The Gewirtz graph is an srg(56, 10, 0, 2)
Strongly_regular_graph
Mathematical concept
In mathematics, when the elements of some set S {\displaystyle S} have a notion of equivalence (formalized as an equivalence relation), then one may naturally
Equivalence_class
Process of repeating items in a self-similar way
linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within
Recursion
Mathematical-logic system
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Property of operations
/ˌɪdɛmˈpoʊtəns/, US: /ˈaɪdəm-/) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without
Idempotence
Generalization of "n-th" to infinite cases
numbers described here. In a broader mathematical sense, counting can be viewed as the instantiation of mathematical induction. To enumerate a well-ordered
Ordinal_number
Impossible task in computing
In mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed
Entscheidungsproblem
Mathematical theory related to general topology
rational sequence topology is specified by letting each rational number singleton to be open, and using as a neighborhood base for each irrational number
Rational_sequence_topology
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS
SINGLETON MATHEMATICS