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Any number that is not an integer but is very close to one
recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers may be considered interesting
Almost_integer
Concept in algebraic number theory
In number theory, Heegner numbers are square-free positive integers d {\displaystyle d} such that the imaginary quadratic field Q ( − d ) {\displaystyle
Heegner_number
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
expressed as a ratio of an integer to a non-zero integer. All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real
List_of_types_of_numbers
Coincidence in mathematics
of Almost Identities, p. 1, arXiv:math/0409014 "Almost Integer". 10 November 2023. Archived from the original on 27 November 2023. "Almost Integer". 1
Mathematical_coincidence
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
Natural number
numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. "13.1.2 Integer Types (Exact Value) - INTEGER, INT, SMALLINT, TINYINT, MEDIUMINT
1,000,000,000
Open problem on 3x+1 and x/2 functions
numbers, multiply by 3 and add 1. With enough repetition, do all positive integers converge to 1? More unsolved problems in mathematics The Collatz conjecture
Collatz_conjecture
Constant e raised to the power of pi
232e.102G. doi:10.1038/scientificamerican0575-102. Eric Weisstein, "Almost Integer" at MathWorld. Waldschmidt, Michel (2021). "Schanuel's Conjecture: algebraic
Gelfond's_constant
Natural number
of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences
1,000,000,000,000
Nearest integers from a number
returns the greatest integer less than or equal to x, written ⌊x⌋ or floor(x). Similarly, the ceiling function returns the least integer greater than or equal
Floor_and_ceiling_functions
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
Natural number
number preceding a cube. As an early prime number in the series of positive integers, the number seven has symbolic associations in religion, mythology, superstition
7
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 22 May 2022. Sloane, N. J. A. (ed.). "Sequence A016064 (Smallest side lengths of almost-equilateral
700_(number)
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)
Number, approximately 2.41421
smaller than 1, thus powers of σ {\displaystyle \sigma } generate almost integers and the sequence σ n mod 1 {\displaystyle \sigma ^{n}{\bmod {1}}} is
Silver_ratio
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
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
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
Irrational numbers which appear to be rational
ratio of two integers. Transcendental numbers like e and π, and noninteger surds such as square root of 2 are irrational.) Almost integer Normal number
Schizophrenic_number
Natural number
, 37. In which e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} almost equals the integer 262537412640768744 = 6403203 + 744. Martin Gardner famously asserted
163_(number)
Function that "converges" to periodicity
commensurable (i.e., with a period vector that is not proportional to a vector of integers). A theorem of Kronecker from diophantine approximation can be used to
Almost_periodic_function
Class of subatomic particle
(/ˈboʊzɒn/ /ˈboʊsɒn/) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). The class of bosons is one of the two fundamental
Boson
In mathematics, with negligible exceptions
Similarly, "almost all" can mean "all (elements of an uncountable set) except for countably many". Examples: Almost all positive integers are greater
Almost_all
Replacing a number with a simpler value
reported result. Rounding is almost unavoidable when reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic;
Rounding
Even integers as sums of two primes
Estermann, T. (1938). "On Goldbach's problem: proof that almost all even positive integers are sums of two primes". Proceedings of the London Mathematical
Goldbach's_conjecture
Natural number
22007 + 20072 is prime 2008 – number of 4 × 4 matrices with nonnegative integer entries and row and column sums equal to 3 2009 = 282 + 352, sum of two
2000_(number)
Type of algebraic integer
Pisot–Vijayaraghavan number (or Pisot number or PV number) is a real algebraic integer greater than 1, all of whose Galois conjugates are less than 1 in absolute
Pisot–Vijayaraghavan_number
Length of expression as combination of 1s
In number theory, the complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions
Integer_complexity
Cuboid whose edges and face diagonals have integer lengths
Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are
Euler_brick
Number system extending the rational numbers
integer (possibly negative), and each a i {\displaystyle a_{i}} is an integer such that 0 ≤ a i < p . {\displaystyle 0\leq a_{i}<p.} A p-adic integer
P-adic_number
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
Computer software bug occurring in 2038
1 January 1970)—and store it in a signed 32-bit integer. When the data type's maximum value is exceeded, the integer will overflow to its minimum value, which
Year_2038_problem
Theory of a class of elliptic curves
as are visible when the period lattice is the Gaussian integer lattice or Eisenstein integer lattice. It has an aspect belonging to the theory of special
Complex_multiplication
Lemma concerning the limit of subadditive sequences
. {\displaystyle a_{n+m}\leq a_{n}+a_{m}+C.} Such a sequence is called almost subadditive. Then, lim n → ∞ a n n = inf n ∈ N a n + C n . {\displaystyle
Fekete's_lemma
640\,768\,743.999\,999\,999\,999\,25\ldots ,} is an almost integer, differing from the nearest integer by approximately 7.5×10−13. (0.000000000001; 1000−4;
Orders_of_magnitude_(numbers)
Integer side lengths of a right triangle
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known
Pythagorean_triple
Number, approximately 1.46557
smaller than 1, thus powers of ψ {\displaystyle \psi } generate almost integers. For example: ψ 11 = 67.000222765... ≈ 67 + 1 / 4489 {\displaystyle
Supergolden_ratio
Quotient of two integers
integers, a numerator p and a nonzero denominator q. For example, 3 7 {\displaystyle {\tfrac {3}{7}}} is a rational number, as is every integer (for
Rational_number
Number, approximately 1.3247
smaller than 1, thus powers of ρ {\displaystyle \rho } generate almost integers. For example: ρ 29 = 3480.0002874... ≈ 3480 + 1 / 3479. {\displaystyle
Plastic_ratio
Number, approximately 2.20557
Encyclopedia of Integer Sequences. OEIS Foundation. (sequence A137421 in the OEIS) Panju, Maysum (2011). "A systematic construction of almost integers" (PDF).
Supersilver_ratio
Natural number
Erdős–Woods number, since it is possible to find sequences of 92 consecutive integers such that each inner member shares a factor with either the first or the
92_(number)
Sum of the inverses of the positive cubes
2\operatorname {lcm} (1,2,\ldots ,n)\cdot a_{n}\in \mathbb {Z} } are integers or almost integers. Many people have tried to extend Apéry's proof that ζ(3) is
Apéry's_constant
Term for computer data consisting only of unformatted characters of readable material
string consisting of "hello", following by 4 bytes that express a binary integer that is supposed to be evaluated in a CPU representation like little endian
Plain_text
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
17th-century conjecture proved by Andrew Wiles in 1994
conjecture, especially in older texts) states that there are no positive integers a , b , c , n {\displaystyle a,b,c,n} with n > 2 {\displaystyle n>2} such
Fermat's_Last_Theorem
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences
100,000
Computer format for representing real numbers
In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar
Fixed-point_arithmetic
Two raised to an integer power
of the form 2n where n is an integer, that is, the result of exponentiation with the number two as the base and integer n as the exponent. In the fast-growing
Power_of_two
Notation for representing a fixed value in source code
as it is written in source code. Almost all programming languages have notations for atomic values such as integers, floating-point numbers, and strings
Literal (computer programming)
Literal_(computer_programming)
Used to count, measure, and label
old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) This property of an integer is called the parity. Any odd number n may
Number
Calculations where numbers' precision is only limited by computer memory
for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of
Arbitrary-precision arithmetic
Arbitrary-precision_arithmetic
Order of bytes in a computer word
particularly of manipulating integer data by computers. In pure form, this is valid for moderately sized non-negative integers, e.g., of C data type unsigned
Endianness
Type of complex number
a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio
Algebraic_number
Number in base-10 numeral system
radix (base). Decimal systems are the global standard for denoting integer and non-integer numbers. The way of denoting numbers in a decimal system is often
Decimal
Natural number
"Sequence A006512 (Greater of twin primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved August 5, 2022. Sloane, N. J. A.
19_(number)
Binary representation for signed numbers
most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. As with the
Two's_complement
Product of two prime numbers
Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Nowicki, Andrzej (2013-07-01), Second numbers
Semiprime
Mapping arbitrary data to fixed-size values
32-bit integer. Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use the value directly, whereas the 64-bit integer Long
Hash_function
Notion of convergence in mathematics
{\displaystyle x} is an integer and 0 {\displaystyle 0} when x {\displaystyle x} is not an integer, and so is discontinuous at every integer. The values of the
Pointwise_convergence
Integer having only small prime factors
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number
Smooth_number
Figurate number
The triangular numbers or triangle numbers are the sequence of positive integers that can be represented as a lattice of points arranged in an equilateral
Triangular_number
Algorithm for public-key cryptography
it is practical to find three very large positive integers e, d, and n, such that for all integers x (0 ≤ x < n), both (xe)d and x have the same remainder
RSA_cryptosystem
Polynomial equation whose integer solutions are sought
a Diophantine equation is a polynomial equation with integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation
Diophantine_equation
Extension of the factorial function
{\displaystyle z} except non-positive integers, and Γ ( n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer n {\displaystyle n} . The
Gamma_function
I/O scheduler for the Linux kernel
requests, so this can lead to situations where the operations executed are almost entirely read requests. This becomes more of an important tunable as write_expire
Deadline_Scheduler
Attribute of data
especially a one which is known as Boolean 1. Almost all programming languages supply one or more integer data types. They may either supply a small number
Data_type
Numbers whose sum of divisors is twice the number minus 1
only known even almost perfect numbers are those of the form 2k for some positive integer k; however, it has not been shown that all almost perfect numbers
Almost_perfect_number
Right triangle with a feature making calculations on the triangle easier
integers. However, infinitely many almost-isosceles right triangles do exist. These are right-angled triangles with integer sides for which the lengths of
Special_right_triangle
Accomplishments in factoring large integers
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography
Integer_factorization_records
Number that is not a ratio of integers
irrational numbers are those that cannot be expressed as the ratio of two integers. Geometrically, when the ratio of lengths of two line segments is an irrational
Irrational_number
Number of subsets of a given size
the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and
Binomial_coefficient
Product of numbers from 1 to n
factorial of a non-negative integer n {\displaystyle n} , denoted by n ! {\displaystyle n!} , is the product of all positive integers less than or equal to
Factorial
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
Number divisible only by 1 and itself
trial division, tests whether n {\displaystyle n} is a multiple of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include
Prime_number
Numbers with many divisors
a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive
Highly_composite_number
Two sets with a small overlap
edition, revised and expanded)", Springer, p. 118 Eric van Douwen. The Integers and Topology. In K. Kunen and J.E. Vaughan (eds) Handbook of Set-Theoretic
Almost_disjoint_sets
the cultural or practical significance of an integer and its mathematical properties. List of integers notable for their cultural meanings 3, significant
List_of_numbers
Central computer component that executes instructions
encoded integer) that the CPU can process in one operation, which is commonly called word size, bit width, data path width, integer precision, or integer size
Central_processing_unit
Modular function in mathematics
terms below q−1. All the Fourier coefficients are integers, which results in several almost integers, notably Ramanujan's constant: e π 163 ≈ 640320 3
J-invariant
Number whose square is a given number
{\displaystyle {\frac {m}{n}}} , where m and n are integers). This is the theorem Euclid X, 9, almost certainly due to Theaetetus dating back to c. 380 BC
Square_root
Set theory concept
Annals of Mathematical Logic 17 (1979) pp 271–288. Eric van Douwen. The Integers and Topology. In K. Kunen and J.E. Vaughan (eds) Handbook of Set-Theoretic
Cardinal characteristic of the continuum
Cardinal_characteristic_of_the_continuum
Matrix form in linear algebra
normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just as reduced echelon form can be used
Hermite_normal_form
Product of an integer with itself
number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is
Square_number
Particle smaller than an atom
of quantum mechanics, can be either a boson (with integer spin) or a fermion (with odd half-integer spin). In the Standard Model, all the elementary fermions
Subatomic_particle
Ten raised to an integer power
of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition
Power_of_10
Natural number
a number, numeral, and grapheme. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property
1
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
Unsolved problem in computer science
input S IF the program outputs a list of distinct integers AND the integers are all in S AND the integers sum to 0 THEN OUTPUT "yes" and HALT This is a polynomial-time
P_versus_NP_problem
Every large even number is either sum of a prime and a semi-prime or two primes
result on the twin prime conjecture. It states that if h is a positive even integer, there are infinitely many primes p such that p + h is either prime or
Chen's_theorem
an integer; X t = X ⌊ t ⌋ , t not an integer; {\displaystyle {\begin{cases}X_{t}\sim \mathrm {Unif} (\{X_{t-1}-1,X_{t-1}+1\}),&t{\mbox{ an integer;}}\\X_{t}=X_{\lfloor
Sample-continuous_process
Number that is abundant but not semiperfect
must be greater than 1021. Sidney Kravitz has shown that for k a positive integer, Q a prime exceeding 2k, and R = 2 k Q − ( Q + 1 ) ( Q + 1 ) − 2 k {\displaystyle
Weird_number
Type of integer sequence
In number theory, a Behrend sequence is an integer sequence whose multiples include almost all integers. The sequences are named after Felix Behrend. If
Behrend_sequence
Date and time representation system widely used in computing
referred to as the Unix epoch. Unix time is typically encoded as a signed integer. The Unix time 0 is exactly midnight UTC on 1 January 1970, with Unix time
Unix_time
Mathematical function
powers over the integers and the prime zeta function a sum of inverse powers of the prime numbers, the k {\displaystyle k} -primes (the integers that are a
Prime_zeta_function
How many integer lattice points there are in a circle
mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius
Gauss_circle_problem
Positive integer that is the product of three distinct prime numbers
theory, a sphenic number (from Ancient Greek: σφήν, 'wedge') is a positive integer that is the product of three distinct prime numbers. For example, since
Sphenic_number
Smooth manifold
well understood. For every integer n, the flat space R2n admits an almost complex structure. An example for such an almost complex structure is (1 ≤ j
Almost_complex_manifold
ordinary differential equations. Hadamard conjecture: for every positive integer k {\displaystyle k} , a Hadamard matrix of order 4 k {\displaystyle 4k}
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Number expressed in the base-2 numeral system
representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with
Binary_number
ALMOST INTEGER
ALMOST INTEGER
Girl/Female
German
Of Noble Spirit
Girl/Female
Biblical
Hidden.
Boy/Male
Czech
Determined; stubborn.
Male
Egyptian
, child of the moon.
Girl/Female
Arabic, Muslim
Diamond
Boy/Male
Christian & English(British/American/Australian)
Lawyer
Girl/Female
Muslim
Diamond. Adamant.
Girl/Female
Indian
A diamond
Girl/Female
Afghan, Arabic, German, Gujarati, Hindu, Indian, Kannada, Kurdish, Malayalam, Marathi, Muslim, Parsi, Punjabi, Sikh, Sindhi
A Diamond; Adamant; Brightness
Male
English
Scottish surname transferred to English forename use, from the medieval Swedish personal name Lagman, LAMONT means "lawman."
Boy/Male
Czech, Czechoslovakian, German
Determined; Stubborn; Sincere
Girl/Female
Swedish
Pearl.
Surname or Lastname
English
English : ostensibly a topographic name containing Middle English cott, cote ‘cottage’ (see Coates). In fact, however, it is generally if not always an alteration of Alcock, in part at least for euphemistic reasons.Louisa May Alcott (1832–88), author of Little Women (1869), was the daughter of Amos Bronson Alcott (1799–1888), who had changed the family name from Alcox. The family trace their descent from an Alcocke family who emigrated from England to MA with John Winthrop in 1629.
Boy/Male
American, Australian, Chinese, Christian, Jamaican, Norse, Scandinavian, Scottish
Lawyer; Law Man; Man of Law
Boy/Male
Hawaiian
Strong (Hawaiian interpretation of the name Amos).
Boy/Male
Norse Scandinavian American Gaelic Scottish
Lawyer.
Boy/Male
American, British, English
From the Old Cottage
Boy/Male
British, English
From the Old Cottage
Boy/Male
Scandinavian
Surname.
Boy/Male
German
Power of an Eagle
ALMOST INTEGER
ALMOST INTEGER
Boy/Male
Hindu, Indian, Marathi
Victory; Success
Boy/Male
Tamil
Prathmesh | பà¯à®°à®¤à®®à¯‡à®·
Lord Ganesh
Boy/Male
Indian, Punjabi, Sikh
One who Takes the Shelter of God
Girl/Female
Arabic, Hindu, Indian, Kannada, Muslim
To Walk with a Swinging Gait
Girl/Female
Celebrity, Gujarati, Hindu, Indian, Kannada, Sanskrit, Traditional
Goddess of Melody; Master of Melodic Modes
Girl/Female
Hindu, Indian
Another Name of Parvati
Boy/Male
Australian, German, Turkish
Honor
Girl/Female
Indian
Beautiful
Girl/Female
Arabic, Muslim
Friendly; Sociable
Girl/Female
Hindu, Indian, Marathi, Tamil
Sinless; Goddess Lakshmi
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
n.
The fruit of the almond tree.
adv.
Nearly; well nigh; all but; for the greatest part.
n.
The European shad (Clupea alosa); -- called also allice shad or allis shad. The name is sometimes applied to the American shad (Clupea sapidissima). See Shad.
n.
The tree that bears the fruit; almond tree.
v. t.
Having wandered from, or unable to find, the way; bewildered; perplexed; as, a child lost in the woods; a stranger lost in London.
v. t.
Parted with; no longer held or possessed; as, a lost limb; lost honor.
v. t.
Not perceptible to the senses; no longer visible; as, an island lost in a fog; a person lost in a crowd.
v. t.
Ruined or destroyed, either physically or morally; past help or hope; as, a ship lost at sea; a woman lost to virtue; a lost soul.
adv.
Nearly; almost; much.
a.
Situated at the farthest point or extremity; farthest out; most distant; extreme; as, the utmost limits of the land; the utmost extent of human knowledge.
a.
Being in the greatest or highest degree, quantity, number, or the like; greatest; as, the utmost assiduity; the utmost harmony; the utmost misery or happiness.
v. t.
Hardened beyond sensibility or recovery; alienated; insensible; as, lost to shame; lost to all sense of honor.
n.
The most that can be; the farthest limit; the greatest power, degree, or effort; as, he has done his utmost; try your utmost.
adv.
Almost; nearly.
adv.
Almost.
adv.
Closely; nearly; almost.
n.
Anything shaped like an almond.
a.
Most distant; farthest.
n.
Alms.
v. t.
Not employed or enjoyed; thrown away; employed ineffectually; wasted; squandered; as, a lost day; a lost opportunity or benefit.