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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
are 0 (if included), 1, 2, 3, and so on. 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
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
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
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
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
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)
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
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
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
Natural number
square triangular number 1,673,196,525 : Least common multiple of the odd integers from 1 to 25 1,677,922,740 : number of series-reduced planted trees with
1,000,000,000
Number, approximately 1.46557
smaller than 1, thus powers of ψ {\displaystyle \psi } generate almost integers. For example: ψ 11 = 67.000222765... {\displaystyle \psi ^{11}=67.000222765
Supergolden_ratio
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
163). In which e π 163 {\displaystyle e^{\pi {\sqrt {163}}}} almost equals the integer 262537412640768744 = 6403203 + 744. Martin Gardner famously asserted
163_(number)
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
Number, approximately 1.83929
smaller than 1, thus powers of τ {\displaystyle \tau } generate almost integers. For example: τ 18 = 58034.99919... {\displaystyle \tau ^{18}=58034
Tribonacci_ratio
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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, approximately 2.20557
smaller than 1, so powers of ς {\displaystyle \varsigma } generate almost integers. For example: ς 10 = 2724.00146856... {\displaystyle \varsigma ^{10}=2724
Supersilver_ratio
Number, approximately 1.32472
smaller than 1, thus powers of ρ {\displaystyle \rho } generate almost integers. For example: ρ 29 = 3480.0002874... {\displaystyle \rho ^{29}=3480
Plastic_ratio
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
Natural number
odd divisors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Weisstein, Eric W. "Almost Prime". mathworld.wolfram.com. Wolfram Research
400_(number)
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
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
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
Sum of the inverses of the positive cubes
polynomials, and the subsequences bn,2lcm(1,2,…,n)⋅an∈ℤ are integers or almost integers. Many people have tried to extend Apéry's proof that ζ(3) is
Apéry's_constant
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
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
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
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)
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
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
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
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
Two raised to an integer power
number of the form 2n where n is an integer, that is, the result of exponentiation with the number 2 as the base and integer n as the exponent. In the fast-growing
Power_of_two
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
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)
Algorithm for computing greatest common divisors
efficient method for computing the greatest common divisor (GCD) of two integers, the largest number that divides them both without a remainder. It is named
Euclidean_algorithm
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)
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
Extension of the factorial function
z} except non-positive integers, and satisfies Γ ( n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer n {\displaystyle n}
Gamma_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
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
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
Arithmetic operation
involving two numbers: the base, b, and the exponent, n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that
Exponentiation
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
Algebraic theory
and an integer n≥1. The indecomposable modules are isomorphic to one of k[x]/(xm) for 1≤ m ≤ n, and the only projective one has m=n. The almost split sequences
Auslander–Reiten_theory
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
Type of permutation of a set of elements
Dn is the nearest integer to n!/e. The above semi-log graph shows that the derangement graph lags the permutation graph by an almost constant value. More
Derangement
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
Number with few prime factors
smallest k-almost prime is 2k. The first few k-almost primes are: The number πk(n) of positive integers less than or equal to n with exactly k prime divisors
Almost_prime
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
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
Classification of algorithm
doi:10.1145/3460351. Harvey, David; van der Hoeven, Joris (March 2019). "Integer multiplication in time O(n log n)". HAL. hal-02070778. Harvey, David (9
Galactic_algorithm
Large cardinal from set theory
the supremum of j n ( κ ) {\displaystyle j^{n}(\kappa )} for positive integers n {\displaystyle n} . However Kunen's inconsistency theorem shows that
Huge_cardinal
Mathematical problem
stated: Given positive integers a1,a2,…,ansuch that gcd(a1,a2,…,an)=1, find the largest integer that cannot be expressed as an integer conical combination
Coin_problem
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
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
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
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
Triangle whose side lengths and area are integers
a triangle whose side lengths a, b, and c and area T are all positive integers. Heronian triangles are named after Heron of Alexandria, based on their
Heronian_triangle
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
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
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
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
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
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
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
Number divisible only by 1 and itself
number n, called trial division, tests whether n is a multiple of any integer between 2 and n. Faster algorithms include the Miller–Rabin primality
Prime_number
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
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
Number representing a continuous quantity
negative numbers. The real numbers include the rational numbers, such as the integer − 5 {\displaystyle -5} and the fraction 4 / 3 {\displaystyle 4/3} . Real
Real_number
On integer partitions from monotonic functions
parts to 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
Lambek–Moser_theorem
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
Certain type of divisor of an integer
from R. Vaidyanathaswamy (1931), who used the term block divisor. The integer 5 is a unitary divisor of 60, because 5 and 60 5 = 12 {\displaystyle {\frac
Unitary_divisor
Numbers significantly larger than those used regularly
redirect targets Power of 10 – Ten raised to an integer power Power of two – Two raised to an integer power Tetration – Arithmetic operation Rayo's number
Large_numbers
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
Application layer protocol
method or response status code. The status code is a three-digit, decimal, integer value that represents the disposition of the server's attempt to satisfy
HTTP
Number whose square is a given number
cannot be written exactly as mn, 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
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
Finitely many for a smooth algebraic curve of genus > 0 defined over a number field
there are only finitely many points on C with coordinates in the ring of integers O of K, provided g > 0. In 1926, Siegel proved the theorem effectively
Siegel's theorem on integral points
Siegel's_theorem_on_integral_points
Way of arriving to a mathematical proof
∎ By definition, if n is an odd integer, it can be expressed as n = 2 k + 1 {\displaystyle n=2k+1} for some integer k. Thus n 2 = ( 2 k + 1 ) 2 = ( 2
Direct_proof
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ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
ALMOST INTEGER
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