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Symbol representing a mathematical concept
systems particularly mathematical logic, a function symbol is a non-logical symbol which represents a function or mapping on the domain of discourse, though
Function_symbol
Set of rules defining correctly structured programs
the language are denoted by non-textual symbols. Most symbols denote functions or operators. A monadic function takes as its argument the result of evaluating
APL_syntax_and_symbols
Symbols requiring interpretation
model. In first-order logic, these usually consist of constant symbols, function symbols, and predicates. This is in contrast to logical constants which
Non-logical_symbol
logical symbols Logic gate § Symbols Logical connective Mathematical operators and symbols in Unicode Non-logical symbol Polish notation Truth function Truth
List_of_logic_symbols
Type of logical system
groups has one constant symbol 0, one unary function symbol −, one binary function symbol +, and one binary relation symbol ≤. Then: The expressions
First-order_logic
Mapping of mathematical formulas to a particular meaning
structure consists of: a set S {\displaystyle S} of function symbols and relation symbols, along with a function ar : S → N 0 {\displaystyle \operatorname {ar}
Structure (mathematical logic)
Structure_(mathematical_logic)
In logic, defining a new symbol
adding a new n {\displaystyle n} -ary function symbol f {\displaystyle f} , the logical axioms featuring the symbol f {\displaystyle f} and the new axiom
Extension_by_definition
the first ◻ {\displaystyle \Box } is the name (symbol) of a function, denotes the value of the function applied to the expression between the parentheses;
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Specially annotated symbol in an object file
annotating symbols as weak, namely a special #pragma, #pragma weak, and, alternatively, a function and variable attribute, __attribute__((weak)). // function declaration
Weak_symbol
Description of non-logical symbols
nullary (0-ary) function symbol as constant symbol, otherwise constant symbols are defined separately. A signature with no function symbols is called a relational
Signature_(logic)
Something that represents an idea, process, or physical entity
only study what a symbol implies but also how it got its meaning and how it functions to make meaning in society. For example, symbols can cause confusion
Symbol
Symbols usually representing media playback controls
control symbols in order to represent the Run, Stop, and Pause functions. Likewise, user interface programing pertaining to these functions has also
Media_control_symbols
Concept in theoretical computer science
with 0 serving as the blank symbol. The machine's transition function takes two inputs: the current non-Halt state, the symbol in the current tape cell,
Busy_beaver
Components of a mathematical or logical formula
constructed from constant symbols, variable symbols, and function symbols. An expression formed by applying a predicate symbol to an appropriate number
Term_(logic)
Symbol showing if electrical power is on
standardized symbols are intended to communicate their function in a language-independent manner. Because the exact meaning of the standby symbol on a given
Power_symbol
Fragment of first-order logic
which all relation symbols in the signature are monadic (that is, they take only one argument), and there are no function symbols. In other words, all
Monadic_predicate_calculus
Formalism of first-order logic
term f ( x 1 , … , x n ) {\displaystyle f(x_{1},\ldots ,x_{n})} whose function symbol f {\displaystyle f} is new. The variables of this term are as follows
Skolem_normal_form
Function in number theory
In number theory, the Legendre symbol is a function of a {\displaystyle a} and p {\displaystyle p} defined as ( a p ) = { 1 if a is a quadratic residue
Legendre_symbol
Assignment of meaning to the symbols of a formal language
interpretation is a function that provides the extension of symbols and strings of an object language. For example, an interpretation function could take the
Interpretation_(logic)
Typographical symbol (@)
The at sign (@) is a typographical symbol used as an accounting and invoice abbreviation meaning "at a rate of" (e.g. 7 widgets @ £2 per widget = £14)
At_sign
Data structure used by a language translator such as a compiler or interpreter
computer science, a symbol table is a data structure where each identifier or symbol (referring to variables, constants, procedures, functions, etc.) in a program's
Symbol_table
Currency sign
emulated with a normal italic small-letter f in most serif typefaces or function symbol in LaTeX notation ( f, f ). It is used in the following current and
Florin_sign
Describes approximate behavior of a function
bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, ∼, Ω, ≪, ≫, ≍, ω, and Θ to
Big_O_notation
Association of one output to each input
defining a function explicitly, such as in "let f ( x ) = sin ( x 2 + 1 ) {\displaystyle f(x)=\sin(x^{2}+1)} ". When the symbol denoting the function consists
Function_(mathematics)
Typographic symbol (#)
The symbol # is known as the number sign, hash, and the pound sign and has a variety of other names. The symbol has historically been used for a wide
Number_sign
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
Dirac measure Heaviside step function Indicator function Levi-Civita symbol Minkowski metric 't Hooft symbol Unit function XNOR gate Nakahara, Mikio (2003)
Kronecker_delta
Freely generated algebraic structure over a given signature
(absolutely freely) defined starting from the set of constants and function symbols in a set of clauses. That is, the Herbrand universe consists of all
Term_algebra
Whether a decision problem has an effective method to derive the answer
equality and either: a predicate symbol of arity no less than 2, or two unary function symbols, or one function symbol of arity no less than 2, established
Decidability_(logic)
Term that does not contain any variables
unary function symbol s {\displaystyle s} for the successor function and a binary function symbol + {\displaystyle +} for addition. s ( 0 ) , s ( s ( 0 )
Ground_expression
Existence and cardinality of models of logical theories
_{0}} representing the arity of function and relation symbols. (A nullary function symbol is called a constant symbol.) In the context of first-order
Löwenheim–Skolem_theorem
Structure over a vocabulary defined solely by syntactical properties
countably infinite if σ {\displaystyle \sigma } is countable and a function symbol of arity greater than 0 exists. In the context of first-order languages
Herbrand_structure
Evaluation of a function on its argument
the theory as a binary function symbol ∙(∙) if desired without any loss of expressiveness by defining: X(Y)={zif X is a function, and (Y,z)∈X∅otherwise
Function_application
Derivative of a function with multiple variables
original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f'x(x,y,…),∂f∂x(x,y,…). The symbol used to
Partial_derivative
3-volume treatise on mathematics, 1910–1913
symbols: "→" (implies, IF-THEN, and "⊃"), "&" (and), "∨" (or), "¬" (not), "∀" (for all), "∃" (there exists); predicate symbol: "=" (equals); function
Principia_Mathematica
Algorithmic process of solving equations
uninterpreted functions (because unification is done on uninterpreted terms), or the theory of constructors (because all function symbols just build up
Unification (computer science)
Unification_(computer_science)
Flow Diagram
“no-go” conditions. These symbols are placed adjacent to lines leaving a particular function to indicate alternative paths. A function shall be represented
Functional_flow_block_diagram
Expected value of a random variable given that certain conditions are known to occur
denoted E ( X ∣ Y = y ) {\displaystyle E(X\mid Y=y)} or a separate function symbol such as f ( y ) {\displaystyle f(y)} is introduced with the meaning
Conditional_expectation
Symbol representing a mathematical object
for denoting values of functions, such as the symbol y in the equation y = f(x), where x is the argument and f denotes the function itself. A variable may
Variable_(mathematics)
Simple logical interpretation
constants and function symbols are assigned very simple meanings. Specifically, every constant is interpreted as itself, and every function symbol is interpreted
Herbrand_interpretation
Twenty-first letter in the Greek alphabet
mechanics as the symbol for bank angle (sometimes represented with the letter theta, which is also used for pitch angle). The work function of a surface,
Phi
Logic programming with constraint satisfaction
expressions. Variables, constants (zero-arity-function symbols), and expressions are terms, as any function symbol applied to terms. In other words, terms are
Constraint_logic_programming
Mathematical symbol denoting a root
radical symbol, which surrounds the argument of the square root function. The OpenType math table allows adding this overline following the radical symbol. The
Radical_symbol
Mathematical symbols (+ and −)
minus sign (−) are mathematical symbols used to denote positive and negative functions, respectively. In addition, the symbol + represents the operation of
Plus_and_minus_signs
Programming construct
is a synonym for function symbol. Callback (computer programming) Closure (computer programming) Function pointer Higher-order function Command pattern
Function_object
Computation model defining an abstract machine
(states); Γ={0,1} (tape alphabet symbols); b=0 (blank symbol); Σ={1} (input symbols); δ= see state-table below (transition function). q0=A (initial state); F={HALT}
Turing_machine
Mathematical symbol for "greater than"
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting
Greater-than_sign
Total order in computer science
where (.>) is a user-given total precedence order on the set of all function symbols. Intuitively, a term f(...) is bigger than any term g(...) built from
Path ordering (term rewriting)
Path_ordering_(term_rewriting)
Axiom in set theory
as the choice function τ is a proper class and in ZFC one cannot quantify over classes. It can be stated by adding a new function symbol τ to the language
Axiom_of_global_choice
Pictogram used to represent various electrical and electronic devices or functions
An electronic symbol is a pictogram used to represent various electrical and electronic devices or functions, such as wires, batteries, resistors, and
Electronic_symbol
Logical problem studied in computer science
function symbols (e.g., f ( f ( u , v ) , v ) = f ( u , v ) {\displaystyle f(f(u,v),v)=f(u,v)} where f {\displaystyle f} is some unspecified function
Satisfiability modulo theories
Satisfiability_modulo_theories
Ghanaian symbols representing concepts or aphorisms
departures in the use of the symbols on items such as T-shirts and jewellery. Adinkra symbols have a decorative function but also represent objects that
Adinkra_symbols
Area of mathematical logic
language is a set of non-logical symbols such that each symbol is either a constant symbol, or a function or relation symbol with a specified arity. Note
Model_theory
Unicode block
symbol. U+2118 ℘ SCRIPT CAPITAL P is a symbol for Weierstrass's elliptic function. It is officially aliased as U+2118 ℘ WEIERSTRASS ELLIPTIC FUNCTION
Mathematical Alphanumeric Symbols
Mathematical_Alphanumeric_Symbols
Class of mathematical functions
℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions, i
Weierstrass_elliptic_function
Mathematical function
(z_{2})>0} . The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol B {\displaystyle
Beta_function
Key on computer keyboards
overlapping and distinct functions dependent on operating system and application. The return key has its origins in two typewriter functions: carriage return
Enter_and_return_keys
Counterexample to the converse of the intermediate value theorem
9+0−−7. Conway's base-13 function takes in a real number x and considers its base-13 representation as a sequence of symbols {0, 1, ..., 9, +, −, .}.
Conway's_base_13_function
System of arithmetic in proof theory
complexity classes have similar properties to EFA: One can omit the binary function symbol exp from the language, by taking Robinson arithmetic together with
Elementary function arithmetic
Elementary_function_arithmetic
Graph data structure
includes the 0-arity function symbols (also called constants), includes the variables, and is closed under application of the function symbols. In other words
E-graph
Property of term rewriting systems
term are completely disjoint—that is, the redexes share no common function symbol. For example, the TRS with reduction rules ρ 1 : f ( x , y ) → g
Orthogonality (term rewriting)
Orthogonality_(term_rewriting)
Summary of a mathematical proof
(and only 15) symbols: A constant symbol 0 for zero. A unary function symbol S for the successor operation and two binary function symbols + and × for addition
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Axioms for the natural numbers
{\displaystyle \mathbb {N} .} The non-logical symbols for the axioms consist of a constant symbol 0 and a unary function symbol S. The first axiom states that the
Peano_axioms
Horizontal line used in mathematical notation
− b + c ¯ {\displaystyle a-{\overline {b+c}}} = a − (b + c) bracketing function Vinculum usage A vinculum or constraint (from Latin vinculum 'fetter, chain
Vinculum_(symbol)
Greek letter
pi (Ⲡ, ⲡ), and Gothic pairthra (𐍀). The uppercase letter Π is used as a symbol for: In textual criticism, Codex Petropolitanus, a 9th-century uncial codex
Pi_(letter)
Eighth letter of the Greek alphabet
during X-ray diffraction The uppercase letter Θ is used as a symbol for: Theta functions Dimension of temperature, by SI standard (in italics) An asymptotically
Theta
Fourth letter in the Greek alphabet
philosophical logic. In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function. The lowercase letter δ (or 𝛿)
Delta_(letter)
Mathematical symbol used to denote integrals and antiderivatives
The integral symbol (see below) is used to denote integrals and antiderivatives in mathematics, especially in calculus. The notation was introduced by
Integral_symbol
Seventh letter in the Greek alphabet
Greek dialects to represent the voiceless glottal fricative, [h]. In this function, it was borrowed in the 8th century BC by the Etruscan and other Old Italic
Eta
Symbols to promote peace
Commissioner of Patents William E. Schuyler Jr, said that the symbol "could not properly function as a trade mark subject to registration by the Patent Office"
Peace_symbols
Expression of symbolic information
{\displaystyle f} is a unary function symbol, P {\displaystyle P} a unary predicate symbol, and Q {\displaystyle Q} a ternary predicate symbol. In modern chemistry
Formula
Logic symbol resembling a "V"
Mathematica, where they called it the Logical Sum or Disjunctive Function. In Unicode the symbol is encoded U+2228 ∨ LOGICAL OR (∨, ∨). In TeX, it is
Descending_wedge
Monetary symbol used in many national currencies
The dollar sign ($; also known as the peso sign) is a currency symbol consisting of a capital ⟨S⟩ crossed with one or two vertical strokes ($ or depending
Dollar_sign
Syntactically correct logical formula
constant symbols, predicate symbols, and function symbols of the theory at hand, along with the arities of the function and predicate symbols. The definition
Well-formed_formula
Impossible task in computing
\cdots \exists \forall \cdots \forall } , equality and relation symbols, and no function symbols. For example, Turing's 1936 paper (p. 263) observed that since
Entscheidungsproblem
Extension of the factorial function
gamma function Multivariate gamma function p-adic gamma function Pochhammer k-symbol Polygamma function q-gamma function Ramanujan's master theorem Spouge's
Gamma_function
Theorem in axiomatic set theory
cofinality function; the gimel function is used for studying the continuum function and the cardinal exponentiation function. The symbol ℷ {\displaystyle
Gimel_function
Class in model theory
is also elementary. Let σ be a signature consisting only of a unary function symbol f. The class K of σ-structures in which f is one-to-one is a basic
Elementary_class
Functions of an angle
mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of
Trigonometric_functions
Function in mathematical logic
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number
Gödel_numbering
Topics referred to by the same term
denoting function composition 0, the number zero ◦, typographical bullet symbol introducing items in a list °, degree symbol ○, gender symbol used to identify
Circle_symbol
Symbolic description of a mathematical object
notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punctuation marks and brackets, used for grouping where
Expression_(mathematics)
Inclusion of one mathematical structure in another, preserving properties of interest
injective, for every n-ary function symbol f∈σ and a1,…,an∈An, we have h(fA(a1,…,an))=fB(h(a1),…,h(an)), for every n-ary relation symbol R∈σ and a1,…,an∈An,
Embedding
Ancient Eurasian icon and Nazi symbol
only secondly it represents the Sun as a reflected function of the North Pole. As such, it is a symbol of life, of the vivifying role of the supreme principle
Swastika
Unicode character block
keyboard. Symbol ⌚ (⌚) is a watch (or clock). Symbol ⏏ (⏏) is the "Eject" button symbol found on electronic equipment. Symbol ⏚ (⏚)
Miscellaneous_Technical
Mathematical functions
special functions (in particular the hypergeometric function) and in the standard reference work Abramowitz and Stegun, the Pochhammer symbol ( x ) n
Falling_and_rising_factorials
Mathematical symbol
and no later than 1232". A monadic × symbol is used by the APL programming language to denote the sign function. The lower-case Latin letter x is sometimes
Multiplication_sign
Concept in combinatorics (part of mathematics)
} which is useful for some of the generating functions of partition functions. The q-Pochhammer symbol is the subject of a number of q-series identities
Q-Pochhammer_symbol
Non-contradiction of a theory
\;Rt_{0}\ldots t_{n-1}\in \Phi ;} for each n {\displaystyle n} -ary function symbol f ∈ S {\displaystyle f\in S} , define f T Φ ( t 0 ¯ … t n − 1 ¯ ) :=
Consistency
Instantaneous rate of change (mathematics)
common notation for differentiation is by using the prime mark in the symbol of a function f(x). This notation, due to Joseph-Louis Lagrange, is now known
Derivative
Symbol used to indicate the del operator
is a triangular symbol resembling an inverted Greek delta: ∇ {\displaystyle \nabla } or ∇. The name comes, by reason of the symbol's shape, from the Hellenistic
Nabla_symbol
Addition of several numbers or other values
or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type
Summation
Eighteenth letter of the Greek alphabet
Eric W. "Weierstrass Sigma Function". mathworld.wolfram.com. Retrieved 25 January 2025. Hill, A. V. (1935). "Units and Symbols". Nature. 136 (3432): 222
Sigma
Symbol rate measurement in telecommunications
telecommunications and electronics, baud (/bɔːd/; symbol: Bd) is a common unit of measurement of symbol rate, which is one of the components that determine
Baud
Database system
correspondence in deductive databases. Function symbols: Logic programming languages allow function symbols to build up complex symbols. This is not allowed in deductive
Deductive_database
Whole number
proper rendering support, you may see question marks, boxes, or other symbols. 0 (zero, /ˈziː.roʊ/) is a number representing an empty quantity. Adding
0
almost surely false. Zero-one law holds for first-order logic (without function symbols), first-order logic extended with fixed point operators and first-order
Zero–one_law_(logic)
Typographical symbol
The prime symbol ′, double prime symbol ″, triple prime symbol ‴, and quadruple prime symbol ⁗ are used to designate units and for other purposes in mathematics
Prime_(symbol)
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
constant symbol cr for every standard real number r, a function symbol fF for every n-ary function F on the standard real numbers, and a predicate symbol PR
Hyperreal_number
Third letter of the Greek alphabet
The uppercase letter Γ is used as a symbol for: In mathematics, the gamma function (usually written as Γ-function) is an extension of the factorial to
Gamma
Linear map or polynomial function of degree one
the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a
Linear_function
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