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Function that takes one argument
In mathematics, a unary function is a function that takes one argument. A unary operation is a special kind of unary function, whose codomain coincides
Unary_function
Topics referred to by the same term
numbers Unary function, a function that takes one argument; in computer science, a unary operator is a subset of unary function Unary operation, a kind
Unary
Mathematical operation with only one operand
example is any function f : A → A {\displaystyle f:A\rightarrow A} , where A is a set; the function f {\displaystyle f} is a unary operation on A
Unary_operation
Number of arguments required by a function
suffix. For example: A nullary function takes no arguments. Example: f ( ) = 2 {\displaystyle f()=2} A unary function takes one argument. Example: f (
Arity
Quickly growing function
{\displaystyle f(f^{n}(x))=f^{n}(f(x))} . Conceiving the Ackermann function as a sequence of unary functions, one can set A m ( n ) = A ( m , n ) {\displaystyle
Ackermann_function
Function computable with bounded loops
recursive functions, namely: For every unary primitive recursive function g, there is an m such that g(n) = f(m,n) for all n, and For every m, the function h(n)
Primitive_recursive_function
Input to a mathematical function
such as f ( x ) = x 2 {\displaystyle f(x)=x^{2}} , is called a unary function. A function of two or more variables is considered to have a domain consisting
Argument_of_a_function
Function that takes two inputs
giving the notion of bilinear transformation above. Arity Unary operation Unary function Binary operation Iterated binary operation Ternary operation
Binary_function
Theories in mathematical logic
constant 0; The unary function, the successor function, here denoted by prefix S, or by prefix σ or postfix ′ elsewhere; Two binary functions, denoted by
List_of_first-order_theories
Base-1 numeral system
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number N, a symbol representing 1 is repeated N times
Unary_numeral_system
Type of logical system
and with only unary predicate symbols. Rabin fragment: FOL with equality, with exactly one unary function symbol, and with only unary predicate symbols
First-order_logic
Programming paradigm
which function definitions do not identify the arguments (or "points") on which they operate. Instead the definitions merely compose other functions, among
Tacit_programming
Function in logic
validity) A concrete function may be also referred to as an operator. In two-valued logic there are 2 nullary operators (constants), 4 unary operators, 16 binary
Truth_function
job is to resolve the diagram into an expression, one in which several unary operators (call them 3+( . ), 2*( . ), ( . )++ and ( . )[ i ]) are competing
Operators_in_C_and_C++
Technique for creating lexically scoped first class functions
of dx, which should be appropriately small. function derivative(f: UnaryFunction, dx: number): UnaryFunction { return x => (f(x + dx) - f(x)) / dx; } Because
Closure (computer programming)
Closure_(computer_programming)
are an important special case. A unary function whose return type is bool is called a predicate, and a binary function whose return type is bool is called
Functional_(C++)
Mapping of mathematical formulas to a particular meaning
elements A {\displaystyle A} together with two binary functions, that can be enhanced with a unary function, and two distinguished elements; but there is no
Structure (mathematical logic)
Structure_(mathematical_logic)
Functions in computability theory
E 0 {\displaystyle E_{0}} is the addition function, and E 1 {\displaystyle E_{1}} is a unary function which squares its argument and adds two. Then
Grzegorczyk_hierarchy
Expression of symbolic information
a formula, provided that f {\displaystyle f} is a unary function symbol, P {\displaystyle P} a unary predicate symbol, and Q {\displaystyle Q} a ternary
Formula
Mathematical operation that combines three elements to produce another element
through 9. Unary operation Unary function Binary operation Iterated binary operation Binary function Median algebra or Majority function Ternary conditional
Ternary_operation
Whether a decision problem has an effective method to derive the answer
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 by Trakhtenbrot
Decidability_(logic)
Performing order of mathematical operations
other spreadsheet applications), unary operations have a higher priority than binary operations; that is, the unary minus has higher precedence than exponentiation
Order_of_operations
the case if one added a unary function exp {\displaystyle \exp } to the language that was interpreted as the exponential function on R {\displaystyle \mathbb
Tarski's exponential function problem
Tarski's_exponential_function_problem
2011 edition of the C++ programming language standard
by std::unique_ptr. Function object base classes (std::unary_function, std::binary_function), adapters to pointers to functions and adapters to pointers
C++11
Statement that is taken to be true
{\displaystyle 0} is a constant symbol and S {\displaystyle S} is a unary function and the following axioms: ∀ x . ¬ ( S x = 0 ) {\displaystyle \forall
Axiom
Aristotelian logic. ternary function A function that takes three arguments or inputs, in contrast to unary and binary functions. ternary relation A relation
Glossary_of_logic
Function that takes one or more functions as an input or that outputs a function
util.function.*; class Main { public static void main(String[] args) { Function<IntUnaryOperator, IntUnaryOperator> twice = f -> f.andThen(f); IntUnaryOperator
Higher-order_function
Set of rules defining correctly structured programs
the IEEE-754 describes them. The Number constructor (used as a function), or a unary + or -, may be used to perform explicit numeric conversion: const
JavaScript_syntax
Numerical calculations carrying along derivatives
the adjoint; fanout in the primal causes addition in the adjoint; a unary function y = f(x) in the primal causes x̄ = ȳ f′(x) in the adjoint; etc. Reverse
Automatic_differentiation
Nearest integers from a number
Floor and ceiling functions In mathematics, the floor function is the function that takes a real number x as input and returns the greatest integer less
Floor_and_ceiling_functions
Class in model theory
complement 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
Elementary_class
Mathematical concept
In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists
Inverse_function
Function returning minus 1, zero or plus 1
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether
Sign_function
Mathematics notation with operators preceding operands
(here the "−" denotes the binary operation of subtraction, not the unary function of sign-change), any well-formed prefix representation is unambiguous
Polish_notation
Product of numbers from 1 to n
factorial function to a continuous function of complex numbers, except at the negative integers, the (offset) gamma function. Many other notable functions and
Factorial
Symbol representing the word "and" (&)
Go, a prefix & is a unary operator denoting the address in memory of the argument, e.g. &x, &func, &a[3]. In C++ and PHP, unary prefix & before a formal
Ampersand
FOSD model of a domain is a tuple of 0-ary functions (called values) and a set of 1-ary (unary) functions called features. This page discusses multidimensional
FOSD_origami
Axioms for the natural numbers
non-logical symbols for the axioms consist of a constant symbol 0 and a unary function symbol S. The first axiom states that the constant 0 is a natural number:
Peano_axioms
Components of a mathematical or logical formula
describes which function symbol sets Fn are inhabited. Well-known examples are the unary function symbols sin, cos ∈ F1, and the binary function symbols +,
Term_(logic)
Well-quasi-ordering of finite trees
A(10)} symbols, where A ( n ) {\displaystyle A(n)} is the unary version of the Ackermann function, but it can be proved to exist in ACA0 with at most 10
Kruskal's_tree_theorem
Operation on mathematical functions
two functions, f {\displaystyle f} and g {\displaystyle g} , and returns a new function f ∘ g {\displaystyle f\circ g} . When the composite function f ∘
Function_composition
Lattice in universal algebra
ternary conditional operator) and the constant unary functions 0 and 1. Moreover, we need the threshold functions t h k n ( x 1 , … , x n ) = { 1 if | { i
Post's_lattice
Summary of a mathematical proof
symbols: A constant symbol 0 for zero. A unary function symbol S for the successor operation and two binary function symbols + and × for addition and multiplication
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Type of mathematical function
would give us an infinite number of functions. So instead, let us merge the unary functions into a binary function. By transfinite recursion on α {\displaystyle
Ordinal_notation
Logarithm to the base of the mathematical constant e
to a multi-valued function: see complex logarithm for more. The natural logarithm function, if considered as a real-valued function of a positive real
Natural_logarithm
In logic, defining a new symbol
{\displaystyle \subseteq } , the constant ∅ {\displaystyle \emptyset } , the unary function symbol P (the power set operation), etc. All of these symbols belong
Extension_by_definition
Generalization of Rice's theorem
unary function θ {\displaystyle \theta } on integers, let C ( θ ) {\displaystyle C(\theta )} denote the 'frustum' of all partial-recursive functions that
Rice–Shapiro_theorem
Axiom in set theory
language extended by the unary function symbol τ, the axiom of constructibility implies that if τ is said explicitly definable function, then this τ is a global
Axiom_of_global_choice
Natural number
{ 0 } {\displaystyle \{0\}} , a set containing only the element 0. The unary numeral system, as used in tallying, is an example of a "base-1" number
1
Mathematical function conceived as a crude model
Research has shown that unary coding is used in the neural circuits responsible for birdsong production. The use of unary in biological networks is
Artificial_neuron
Topics referred to by the same term
twelve-tone musical technique Derivation (differential algebra), a unary function satisfying the Leibniz product law Formal proof or derivation, a sequence
Derivation
Set with operations obeying given axioms
elements (higher arity operations) and operations that take only one argument (unary operations) or even zero arguments (nullary operations). The examples listed
Algebraic_structure
Mathematical system
Individual terms are formed from the constant 0, the unary function S (the successor function), and the binary operations + and ⋅ {\displaystyle \cdot
Second-order_arithmetic
Replacing subterm in a formula with another term
undecidable. Termination is also undecidable for systems using only unary function symbols; however, it is decidable for finite ground systems. The following
Rewriting
Structure over a vocabulary defined solely by syntactical properties
{\displaystyle T} . For a constant symbol c {\displaystyle c} and a unary function symbol f ( ⋅ ) {\displaystyle f(\,\cdot \,)} we have the following interpretation:
Herbrand_structure
Addition, multiplication, division, ...
with a partial mapping in place of a function. There are two common types of operations: unary and binary. Unary operations involve only one value, such
Operation_(mathematics)
Piecewise function that clamps its input to be non-negative
The ramp function is a unary real function, whose graph is shaped like a ramp. It can be expressed by numerous definitions, for example "0 for negative
Ramp_function
How software progresses through its implementation
STL, there is a std::for_each template function which can iterate on STL containers and call a unary function for each element. The functionality also
Control_flow
Term that does not contain any variables
numbers 0 and 1, respectively, a unary function symbol s {\displaystyle s} for the successor function and a binary function symbol + {\displaystyle +} for
Ground_expression
Property of operations
negation function ¬ {\displaystyle \neg } on the Boolean domain is not idempotent, but ¬ ∘ ¬ {\displaystyle \neg \circ \neg } is. Similarly, unary negation
Idempotence
Mathematical function that can be computed by a program
{Blue}f\circ g} if f is unary, max(f,g), min(f,g), arg max{y ≤ f(x)} and many more combinations. The following examples illustrate that a function may be computable
Computable_function
Mathematical table used in logic
zero operands and therefore no input values There are 2 unary operations: Unary identity Unary negation Logical identity is an operation on one logical
Truth_table
Mathematical symbols (+ and −)
unary minus, which binds more strongly than multiplication or division. However, in some programming languages (Microsoft Excel in particular), unary
Plus_and_minus_signs
Programming construct
recently, symbols (accessed via the literal unary indicator :) can also be converted to Procs. Using Ruby's unary & operator—equivalent to calling to_proc
Function_object
Basic programming language construct
unary operators, with a few supporting more operands, such as the ?: operator in C, which is ternary. There are prefix unary operators, such as unary
Operator (computer programming)
Operator_(computer_programming)
Function with a smaller domain
multivalued function. In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation
Restriction_(mathematics)
Repeated application of an operation to a sequence
correspond to higher-order functions such as fold or reduce. Unary operation Unary function Binary operation Binary function Ternary operation Saunders
Iterated_binary_operation
Formula for the derivative of an inverse function
denotes the unary derivative operator (on the space of functions) and ∘ {\displaystyle \circ } denotes function composition. Geometrically, a function and inverse
Inverse_function_rule
0-ary functions or transformations called values: f -- base program with feature f h -- base program with feature h and features are unary functions/transformations
Feature-oriented_programming
Formal language in computational complexity theory
In computational complexity theory, a unary language or tally language is a formal language (a set of strings) where all strings have the form 1k, where
Unary_language
Recursive function
catamorphic parts. The anamorphic part can be defined in terms of a unary function g : A → B × A {\displaystyle g:A\rightarrow B\times A} defining the
Hylomorphism (computer science)
Hylomorphism_(computer_science)
Concept in theoretical computer science
In other words, this is the largest unary number a Turing machine of n states can write on a tape. The function space ( n ) {\displaystyle {\text{space}}(n)}
Busy_beaver
Combinational logic circuit
decoder function is available in standard ICs such as the CMOS 4511. A binary to unary decoder converts each binary value to its associated unary representation
Binary_decoder
Number which when multiplied by x equals 1
reciprocal function, the function f(x) that maps x to 1 x , {\displaystyle {\tfrac {1}{x}},} is one of the simplest examples of a function which is its
Multiplicative_inverse
{\displaystyle a_{1},a_{2},a_{3},\ldots \,} . There are no function symbols. The predicate symbols can be unary, binary or of higher arities. The finite set of predicate
Pure_inductive_logic
Property that assigns truth values to k-tuples of individuals
(such as that of having been awarded the Nobel Prize). Every nullary function is a unary relation. Binary (2-ary) relations are the most commonly studied
Finitary_relation
the symbol f appears once as binary, and once as unary, which is illicit, as Arity must be a function. Comon, Hubert; Dauchet, Max; Gilleron, Rémi; Jacquemard
Ranked_alphabet
Type of data structure
be "unary". Examples are the negative sign (when nothing is put on the left of it) and the "logical NOT" (exclamation mark, !). Sender of unary operators
C++_classes
Product of a number by itself
the square function satisfies the identity x2 = (−x)2. This can also be expressed by saying that the square function is an even function. The squaring
Square_(algebra)
Term in mathematical logic
second-order logic with a unary function. It is also the set of spectra of monadic second-order logic with the successor function. Fagin's theorem is a result
Spectrum_of_a_sentence
Number whose square is a given number
square root function f ( x ) = x {\displaystyle f(x)={\sqrt {x}}} (usually just referred to as the "square root function") is a function that maps the
Square_root
Symbol connecting formulas in logic
constants True and False can be thought of as nullary operators. Negation is a unary connective, and so on. Commonly used logical connectives include the following
Logical_connective
Calculator software
binary functions, such as the four basic arithmetic operations. Unlike many other calculators, it uses prefix notation, not postfix notation for unary functions
GNOME_Calculator
Mathematical structure
..., but no infinite ascending ones. If f is a binary function symbol, g is a unary function symbol, and x and y denote variables, then the terms f(x
Subsumption_lattice
Mathematical set of all subsets of a set
that its operations are unary. A multigraph has two sorts of elements forming a set V of vertices and E of edges, and has two unary operations s, t : E →
Power_set
Arithmetic operation
three functions are elementary. The first four hyperoperations are shown here, with tetration being considered the fourth in the series. The unary operation
Tetration
Boolean function
the tie can be broken randomly. For n = 1 the median operator is just the unary identity operation x. For n = 3 the ternary median operator can be expressed
Majority_function
Description of non-logical symbols
define the function symbols of the signature as something like f 2 {\displaystyle f_{2}} (which is binary), f 1 {\displaystyle f_{1}} (which is unary) and f
Signature_(logic)
Greek letter
pi bond. The natural projection on the tangent bundle on a manifold. The unary operation of projection in relational algebra. Sometimes an element of a
Pi_(letter)
Reversal of the order of elements of a binary relation
that for an inverse function. Although many functions do not have an inverse, every relation does have a unique converse. The unary operation that maps
Converse_relation
Theorem 12.16 in ) MSO (see Exercice 12.6 in ) First-order logic with unary function symbols does not have the zero-one law, but has the convergence law
Zero–one_law_(logic)
(0,S) consisting of an element 0 ∈ N and a unary function S : N → N belongs to N × P(N × N) (since a function is a subset of the Cartesian product). A triple
Equivalent definitions of mathematical structures
Equivalent_definitions_of_mathematical_structures
Framework for studying interactive computational tasks through logic
established in the literature. Below are some examples. Let f be a unary function. The problem of computing f will be written as ⊓x⊔y(y=f(x)). According
Computability_logic
Recursion without calling a function by name
functions. This is particularly important for the lambda calculus, which has anonymous unary functions, but is able to compute any recursive function
Anonymous_recursion
Number that, when added to the original number, yields the additive identity
often referred to as the opposite number, or the negative of a number. The unary operation of arithmetic negation is closely related to subtraction and is
Additive_inverse
System including an indeterminate value
Boolean connectives to a trivalent context. Boolean logic allows 22 = 4 unary operators; the addition of a third value with two inputs is 32 = 9 and with
Three-valued_logic
Topics referred to by the same term
usage, application of advanced analytical methods to make better decisions Unary operation, an operation with only one operand Rail transport operations
Operation
tree genetic programming, program composed of a variable number of unary functions and a single terminal. Note that linear tree GP differs from bit string
Linear_genetic_programming
Mathematics
t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into
Construction_of_t-norms
Set-theoretic function
consistently computed in the sub-structure and the large structure. The case of a unary operation is similar; but one should also look at nullary operations, which
Inclusion_map
UNARY FUNCTION
UNARY FUNCTION
Biblical
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Male
Egyptian
, the son of the functionary Heknofre.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, an Egyptian functionary.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
Male
Egyptian
, Functionary of the Interior.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, a great functionary.
UNARY FUNCTION
UNARY FUNCTION
Girl/Female
Tamil
Ultimate
Boy/Male
Indian, Punjabi, Sikh
Embodiment of Peace
Boy/Male
Afghan, African, Arabic, Gujarati, Hindu, Indian, Kannada, Malaysian, Marathi, Muslim, Swahili
Rivulet; Small River
Girl/Female
Hebrew
Father of many.
Boy/Male
Indian
Unique, Unprecedented
Boy/Male
Indian, Punjabi, Sanskrit, Sikh
Joy of Love; Immortal Nectar of God; Immortality; Peace
Boy/Male
Arabic, Muslim
Bright
Boy/Male
Hindu
One who removes parijath flower
Girl/Female
Arabic, Muslim
Gazelle; Deer
Boy/Male
Tamil
Victory
UNARY FUNCTION
UNARY FUNCTION
UNARY FUNCTION
UNARY FUNCTION
UNARY FUNCTION
n.
The quality or state of being unwary; carelessness; heedlessness.
n.
The herb moonwort or "honesty".
n.
The herb lunary or honesty. See Honesty.
n.
One easily deceived in buying stocks; an inexperienced and unwary jobber.
a.
Not vigilant against danger; not wary or cautious; unguarded; precipitate; heedless; careless.
n.
A snare of insidious meshes designed to catch the ignorant and unwary.
n.
A low fleshy fern (Botrychium Lunaria) with lunate segments of the leaf or frond.
n.
Unwary; incautious; unheeding; careless; unaware.
a.
Lunar.
a.
Made or contrived for getting small sums of money from the ignorant or unwary; as, a catchpenny book; a catchpenny show.
v. i.
To puff off, or lay down, one's arms or armor.
superl.
Unwary; unready.
a.
Destitute of function, or of an appropriate organ. Darwin.
adv.
In an unwary manner.
a.
Satin flower; the name of two cruciferous herbs having large flat pods, the round shining partitions of which are more beautiful than the blossom; -- called also lunary and moonwort. Lunaria biennis is common honesty; L. rediva is perennial honesty.
a.
Resembling, or consisting of, snares; entangling; insidious.
n.
One charged with the performance of a function or office; as, a public functionary; secular functionaries.
v. t.
To disarm.
a.
Unexpected; unforeseen; unware.
pl.
of Functionary