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Nearest integers from a number
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 than
Floor_and_ceiling_functions
Topics referred to by the same term
Integer function may refer to: Integer-valued function, an integer function Floor function, sometimes referred as the integer function, INT Arithmetic
Integer_function
Extension of the factorial function
{\displaystyle \Gamma (n)=(n-1)!} for every positive integer n {\displaystyle n} . The gamma function can be defined via a convergent improper integral
Gamma_function
Replacing a number with a simpler value
especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines;
Rounding
Family of solutions to related differential equations
is an integer or a half-integer. When α {\displaystyle \alpha } is an integer, the resulting Bessel functions are often called cylinder functions or cylindrical
Bessel_function
mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member
Integer-valued_function
Method to solve optimization problems
integral objective function c, the optimal value of the linear program { max c x ∣ x ∈ P } {\displaystyle \{\max cx\mid x\in P\}} is an integer. Integral linear
Linear_programming
Mathematical optimization problem restricted to integers
are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints
Integer_programming
Online database of integer sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Function in mathematical number theory
a branch of mathematics, the Carmichael function λ(n) of a positive integer n is the smallest positive integer m such that a m ≡ 1 ( mod n ) {\displaystyle
Carmichael_function
Arithmetic function related to the divisors of an integer
theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts the number
Divisor_function
Number of partitions of an integer
partition function p(n) represents the number of possible partitions of a non-negative integer n. For instance, p(4) = 5 because the integer 4 has the
Partition function (number theory)
Partition_function_(number_theory)
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
Constants of the mathematical zeta function
It also includes derivatives and some series composed of the zeta function at integer arguments. The same equation in s {\displaystyle s} above also holds
Particular values of the Riemann zeta function
Particular_values_of_the_Riemann_zeta_function
Decomposition of an integer as a sum of positive integers
partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only
Integer_partition
Analytic function in mathematics
Riemann sphere the zeta function has an essential singularity. For sums involving the zeta function at integer and half-integer values, see rational zeta
Riemann_zeta_function
Integer that divides another integer
mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may
Divisor
Functions such that f(–x) equals f(x) or –f(x)
n is an odd integer. Even functions are those real functions whose graph is self-symmetric with respect to the y-axis, and odd functions are those whose
Even_and_odd_functions
Number of integers coprime to and less than n
_{e}(x)} . In number theory, Euler's totient function counts the positive integers up to a given integer n {\displaystyle n} that are relatively prime
Euler's_totient_function
Quickly growing function
function (which had three non-negative integer arguments), many authors modified it to suit various purposes, so that today "the Ackermann function"
Ackermann_function
Fast-growing function
function is a mathematical function defined by Harvey Friedman. It is defined by SSCG ( k ) {\displaystyle {\text{SSCG}}(k)} as the largest integer n
Friedman's_SSCG_function
Mapping arbitrary data to fixed-size values
(reinterpreted as an integer) as the hashed value. The cost of computing this identity hash function is effectively zero. This hash function is perfect, as
Hash_function
Degree of differentiability of a function or map
smoothness of a function or map describes the extent to which it has derivatives that exist and vary continuously. Given a non-negative integer k {\displaystyle
Smoothness
Function that can be written as a sum over prime factors
an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to
Additive_function
Number-theoretical function
theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n {\displaystyle n} as
Sum_of_squares_function
Number used for counting
2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set
Natural_number
Mathematical constants
gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer, half-integer, and some
Particular values of the gamma function
Particular_values_of_the_gamma_function
Complex number whose mapping on a coordinate plane produces a triangular lattice
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the
Eisenstein_integer
Non-cryptographic hash function
8-bit unsigned integer. As an example, consider the 64-bit FNV-1 hash: All variables, except for byte_of_data, are 64-bit unsigned integers. The variable
Fowler–Noll–Vo_hash_function
Special mathematical function defined as sin(x)/x
normalized sinc function are the nonzero integer values of x. The function has also been called the cardinal sine or sine cardinal function. The term "sinc"
Sinc_function
Root of a quadratic polynomial with a unit leading coefficient
theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it is a root
Quadratic_integer
Arithmetic operation
numbers: the base, b, and the exponent or power, n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that
Exponentiation
Special mathematical function
of positive integer order arise in the calculation of processes represented by higher-order Feynman diagrams. The polylogarithm function is equivalent
Polylogarithm
lowest integer that is not lesser than x. ⌊□⌉ Nearest integer function: if x is a real number, ⌊ x ⌉ {\displaystyle \lfloor x\rceil } is the integer that
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
positive integers <= 17 Egyptian fraction 1013 = Sophie Germain prime, centered square number, Mertens function zero 1014 = 210-10, Mertens function zero
1000_(number)
Number without repeated prime factors
In mathematics, a square-free integer (or squarefree integer) is an integer that is divisible by no square number other than 1. That is, its prime factorization
Square-free_integer
Computational operation
languages – C. ISO, IEC. 1990. sec. 7.5.6.4. The fmod function returns the value x - i * y, for some integer i such that, if y is nonzero, the result has the
Modulo
the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line Linear function: First degree polynomial
List of mathematical functions
List_of_mathematical_functions
Association of one output to each input
recursive functions are partial functions from integers to integers that can be defined from constant functions, successor, and projection functions via the
Function_(mathematics)
Function on an integer n which is log(p) if n equals p^k and zero otherwise
Mangoldt function, denoted by Λ ( n ) {\displaystyle \Lambda (n)} , is defined as Λ ( n ) = { log p if n = p k for some prime p and integer k ≥ 1
Von_Mangoldt_function
Type of mathematical expression
addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of
Polynomial
Number in {..., –2, –1, 0, 1, 2, ...}
a positive integer Complex integer Hyperinteger Integer complexity Integer lattice Integer part Integer sequence Integer-valued function Mathematical
Integer
Data types supported by the C programming language
type, and also provides macros for true and false. _Bool functions similarly to a normal integer type, with one exception: any conversion to a _Bool gives
C_data_types
Types of special mathematical functions
Γ-function, that the first two factors capture the singularities of γ ( s , z ) {\displaystyle \gamma (s,z)} (at z = 0 or s a non-positive integer), whereas
Incomplete_gamma_function
Multivalued function in mathematics
each integer k {\displaystyle k} there is one branch, denoted by W k ( z ) {\displaystyle W_{k}\left(z\right)} , which is a complex-valued function of one
Lambert_W_function
Open problem on 3x+1 and x/2 functions
positive integer: If the number is even, divide it by two. If the number is odd, triple it and add one. In modular arithmetic notation, define the function f
Collatz_conjecture
This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to
List_of_integer_sequences
Solution of a confluent hypergeometric equation
for integer b, it has the advantage that it can be extended to any integer b by continuity. Unlike Kummer's function which is an entire function of z
Confluent hypergeometric function
Confluent_hypergeometric_function
Largest integer that divides given integers
of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest
Greatest_common_divisor
Solutions of Legendre's differential equation
called the degree and order of the relevant function, respectively. The polynomial solutions when λ is an integer (denoted n), and μ = 0 are the Legendre
Legendre_function
Property of being an even or odd number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For
Parity_(mathematics)
Integers have unique prime factorizations
factorization theorem and prime factorization theorem, states that every integer greater than 1 is either prime or can be represented uniquely as a product
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Natural number
= 37 – 27 2060 – sum of the totient function for the first 82 integers 2061 – Number of sets of positive integers with arithmetic mean 7 2062 = ϕ ( ϕ
2000_(number)
Mathematical sequences
{\displaystyle \operatorname {Fe} (n)=F_{n}} for even integers n {\displaystyle n} . Similarly, the analytic function: Fo ( x ) = φ x + φ − x 5 {\displaystyle
Generalizations of Fibonacci numbers
Generalizations_of_Fibonacci_numbers
Computation modulo a fixed integer
mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when reaching
Modular_arithmetic
Set of rules defining correctly structured programs
interpreted according to use. For example, ⌊3.2 gives 3, the largest integer not above the argument, and 3⌊2 gives 2, the lower of the two arguments
APL_syntax_and_symbols
Natural number
It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number. It is also the first
900_(number)
Function with a multiplicative scaling behaviour
degree of homogeneity, or simply the degree. That is, if k is an integer, a function f of n variables is homogeneous of degree k if f ( s x 1 , … , s
Homogeneous_function
Inverse functions of sin, cos, tan, etc.
-\arctan(x)}{\pi }}\right)\,.} The function rni {\displaystyle \operatorname {rni} } rounds to the nearest integer. For angles near 0 and π, arccosine
Inverse trigonometric functions
Inverse_trigonometric_functions
Rational number equal to an integer plus 1/2
mathematics, a half-integer is a number of the form n + 1 2 , {\displaystyle n+{\tfrac {1}{2}},} where n {\displaystyle n} is an integer. For example, 4 1
Half-integer
Function that is holomorphic on the whole complex plane
positive constants and n {\displaystyle n} is a non-negative integer. An entire function f {\displaystyle f} satisfying the inequality | f ( z ) | ≤ M
Entire_function
Function whose domain is the positive integers
arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range is a subset of the
Arithmetic_function
Numbers obtained by adding the two previous ones
closest integer to φ n 5 {\displaystyle {\frac {\varphi ^{n}}{\sqrt {5}}}} . Therefore, it can be found by rounding, using the nearest integer function: F
Fibonacci_sequence
Datum of integral data type
computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may
Integer_(computer_science)
Natural number
pentagonal number. 392 = 23 × 72, Achilles number. 393 = 3 × 131, Blum integer, Mertens function returns 0. 394 = 2 × 197 = S5 a Schröder number, nontotient, noncototient
300_(number)
Use of functions that call themselves
which computes the greatest common divisor of two integers, can be written recursively. Function definition: gcd ( x , y ) = { x if y = 0 gcd ( y ,
Recursion_(computer_science)
Arithmetic operation
{\displaystyle x=\mathrm {ssrt} (\mathrm {ssrt} (y^{x}))} . For each integer n > 2, the function nx is defined and increasing for x ≥ 1, and n1 = 1, so that the
Tetration
Permutation of the elements of a set in which no element appears in its original position
\left[x\right]} is the nearest integer function and ⌊ x ⌋ {\displaystyle \left\lfloor x\right\rfloor } is the floor function. Other related formulas include
Derangement
Functions of an angle
\sin(x+y).} A positive integer appearing as a superscript after the symbol of the function denotes exponentiation, not function composition. For example
Trigonometric_functions
Natural number
southern Alberta. 404 = 22 × 101, Mertens function returns 0, nontotient, noncototient, number of integer partitions of 20 with an alternating permutation
400_(number)
Function defined by a hypergeometric series
The series terminates if either a or b is a nonpositive integer, in which case the function reduces to a polynomial: 2 F 1 ( − m , b ; c ; z ) = ∑ n
Hypergeometric_function
C function to format and output text
standard library function and is also a Linux terminal (shell) command that formats text and writes it to standard output. The function accepts a format
Printf
Function used in signal processing
processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside
Window_function
Ordered list of whole numbers
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula
Integer_sequence
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A059377 (Jordan function J_4(n))". The On-Line Encyclopedia of Integer Sequences
600_(number)
Mathematical formula involving a given set of operations
variables, and a set of functions considered as basic and connected by arithmetic operations (+, −, ×, /, and integer powers) and function composition. Commonly
Closed-form_expression
Product of two distinct primes ≡ 3 (mod 4)
form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. This means that the factors of a Blum integer are Gaussian primes
Blum_integer
Natural number
number 849 = 3 × 283, the Mertens function of 849 returns 0, Blum integer 850 = 2 × 52 × 17, the Mertens function of 850 returns 0, nontotient, the sum
800_(number)
Decomposition of a number into a product
decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater
Integer_factorization
Integer
inside the function f, its inverse will yield an inverse image, or preimage, of that subset under the function. Exponentiation to negative integers can be
−1
Algorithm in computational number theory
Macaulay2 as the function LLL in the package LLLBases Magma as the functions LLL and LLLGram (taking a gram matrix) Maple as the function IntegerRelations[LLL]
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Mathematical function whose derivative exists
such a function allows one to obtain a function that is differentiable only a finite number of times, the finite number being any positive integer. Given
Differentiable_function
On integer partitions from monotonic functions
the Lambek–Moser theorem. One part states any two non-decreasing integer functions that are inverse, in a certain sense, can be used to split the natural
Lambek–Moser_theorem
Finite or infinite ordered list of elements
sequence. A function from Z {\displaystyle \mathbb {Z} } the set of all integers, into a set, for example the sequence of all even integers (..., −4, −2
Sequence
present, one for integers fitting the native word size minus any tag bit (SmallInteger) and one supporting arbitrary sized integers (LargeInteger). Arithmetic
Comparison of programming languages (basic instructions)
Comparison_of_programming_languages_(basic_instructions)
Algebra of formal sums
represent an element of a free abelian group is as a function from B {\displaystyle B} to the integers with finitely many nonzero values; for this functional
Free_abelian_group
Number whose square is a given number
positional notation system. The square roots of small integers are used in both the SHA-1 and SHA-2 hash function designs to provide nothing up my sleeve numbers
Square_root
Function that is continuous everywhere but differentiable nowhere
integer A and B; that is, rational multipliers of π {\displaystyle \ \pi \ } with an odd numerator and denominator. On these points, the function
Weierstrass_function
Integer having a non-trivial divisor
number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has at least one
Composite_number
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
Form of text that defines C code
standard integer types as implemented on any specific platform. In addition to the standard integer types, there may be other "extended" integer types,
C_syntax
Natural number
290 theorems describes integer-quadratic matrices that describe all positive integers, by the set of the first fifteen integers, or equivalently, the first
29_(number)
Special functions of several complex variables
sum converges. This analytic function can be used to solve a combinatorics problem: in how many different ways can an integer be written as the sum of two
Theta_function
Arithmetic operation
This is the floor function applied to case 2 or 3. It is sometimes called integer division, and denoted by "//". Dividing integers in a computer program
Division_(mathematics)
Attribute of data
denoting functions taking an integer and returning a Boolean. In C, a function is not a first-class data type but function pointers can be manipulated
Data_type
Subroutine call performed as final action of a procedure
factorial: function factorial(n::Integer, a::Integer)::Integer if n == 0: return a else return factorial(n - 1, n * a) end end function factorial(n::Integer)::Integer
Tail_call
Function uniquely mapping two numbers into a single number
in set theory to prove that integers and rational numbers have the same cardinality as natural numbers. A pairing function is a bijection π : N × N → N
Pairing_function
Characterization of how many integers are prime
among positive integers of at most 2000 digits, about one in 4600 is prime (log(102000) ≈ 4605.2). Let π(x) be the prime-counting function defined to be
Prime_number_theorem
Natural number, composite number
non-trivial zero in the Riemann zeta function is 14 {\displaystyle 14} , in equivalence with its nearest integer value, from an approximation of 14.1347251417
14_(number)
Problem of inverting exponentiation in groups
analogous to the one between integer factorization and integer multiplication. Both asymmetries (and other possibly one-way functions) have been exploited in
Discrete_logarithm
INTEGER FUNCTION
INTEGER FUNCTION
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.
Boy/Male
Muslim
To wait
Boy/Male
German, Norse, Swedish
Guarded by Ing; Ing's Beauty
Girl/Female
American, Australian, Danish, Finnish, German, Scandinavian, Swedish, Teutonic
Guarded by Ing; Ing is Beautiful; Daughter of Hero; Enclosure
Female
Scandinavian
Scandinavian form of Old Norse Ingigerðr, INGEGERD means "Ing's enclosure."
Biblical
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Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
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.
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 (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.
Male
Celtic
, great justiciary, or functionary.
Girl/Female
Danish, Finnish, German, Swedish
Guarded by Ing; Ing's Beauty; Ing's Place
Girl/Female
Scandinavian Teutonic Danish Swedish
Ing's abundance. Feminine of Ing who was Norse mythological god of the earth's fertility.
Male
Egyptian
, a high Egyptian functionary.
Male
Egyptian
, Functionary of the Interior.
Boy/Male
Norse
Son's army.
Male
Egyptian
, a great functionary.
Female
Swedish
Swedish contracted form of Scandinavian Ingegerd, INGER means "Ing's enclosure."
Boy/Male
Arabic, Muslim
To Wait
INTEGER FUNCTION
INTEGER FUNCTION
Girl/Female
British, Dutch, English, Finnish, Hebrew, Jamaican
God; God has Listen; Told by God; His Name is God; Heard of God; Believer of God
Girl/Female
Tamil
Good looking
Boy/Male
Muslim
Beautiful, Magnificent, Shining
Girl/Female
Hindu, Indian
Lit by Lamps
Boy/Male
Indian, Telugu
An Ancient Guru (Rushi)
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Lord Shiva
Boy/Male
Hindu, Indian
God's Name
Boy/Male
Muslim
Extreme power
Girl/Female
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sanskrit, Tamil, Telugu
Inspiring; Inspiration; Encouragement
Boy/Male
Spanish
God strengthens.
INTEGER FUNCTION
INTEGER FUNCTION
INTEGER FUNCTION
INTEGER FUNCTION
INTEGER FUNCTION
v. t.
To deposit, as a dead body, in the earth; to bury; to inter.
v. t.
To inter again.
v. t.
To inter with funeral rites; to bury.
n.
A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
n.
One who inters.
n.
That number placed below the line in vulgar fractions which shows into how many parts the integer or unit is divided.
a.
Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
n.
One who intends.
n.
One who makes an entrance or beginning.
imp. & p. p.
of Inter
p. pr. & vb. n.
of Inter
v. t.
To inter.
v. t.
To deposit or inter in a chapel; to enshrine.
n.
One who gathers the vintage.
v. t.
To bury; to inter; to entomb; as, obscurely sepulchered.
v. t.
To deposit and cover in the earth; to bury; to inhume; as, to inter a dead body.
v. t.
To inhume; to bury; to inter.
v. t.
To place in a tomb; to bury; to inter; to entomb.
n.
One who makes an index.