An irreducible fraction is a fraction in which the numerator and denominator are integers that have no other common divisors than 1. In other words, a fraction a/b is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials. Every rational number can be represented as an irreducible fraction with positive denominator in exactly one way.
In mathematics, integer factorization is the 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 than 1, in which case it is called a composite number, or it is not, in which case it is called a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way. If one of the factors is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4). Continuing this process until every factor is prime is called prime factorization; the result is always unique up to the order of the factors by the prime factorization theorem.
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers0, 1, 2, 3, ..., while others start with 1, defining them as the positive integers1, 2, 3, .... Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers plus zero. In other cases, the whole numbers refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary school education, and are ambiguous as well although typically start at 1.
In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. A set may have a finite number of elements or be an infinite set. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.
6 (six) is the natural number following 5 and preceding 7. It is a composite number and the smallest perfect number.
33 (thirty-three) is the natural number following 32 and preceding 34.
In computer science, primitive data types are a set of basic data types from which all other data types are constructed. Specifically it often refers to the limited set of data representations in use by a particular processor, which all compiled programs must use. Most processors support a similar set of primitive data types, although the specific representations vary. More generally, primitive data types may refer to the standard data types built into a programming language. Data types which are not primitive are referred to as derived or composite.
666 is the natural number following 665 and preceding 667.
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 at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009, and is its chairman.
In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains a k-term arithmetic progression for every k. Endre Szemerédi proved the conjecture in 1975.
In mathematics, an element of a set is any one of the distinct objects that belong to that set. For example, given a set called A containing the first four positive integers, one could say that "3 is an element of A", expressed notationally as .
216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.
James Phillip McAuley was an Australian academic, poet, journalist, literary critic, and a prominent convert to Roman Catholicism. He was involved in the Ern Malley poetry hoax.
In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemerédi's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.
Gary Gregory Gach is an American author, translator, editor, and teacher living in San Francisco. His work has been translated into several languages, and has appeared in several anthologies and numerous periodicals. He has hosted Zen Mindfulness Fellowship weekly for 12 years, and he swims in the San Francisco Bay. His work has appeared in The Atlantic, BuddhaDharma, Coyote’s Journal, Harvard Divinity Bulletin, Hambone, In These Times, Lilipoh, Mānoa, The Nation, The New Yorker, Words without Borders, Yoga Journal, and Zyzzyva.
An aperiodic finite-state automaton is a finite-state automaton whose transition monoid is aperiodic.
In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.
In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value. Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spin. Every observed subatomic particle is either a boson or a fermion. Paul Dirac coined the name boson to commemorate the contribution of Satyendra Nath Bose, an Indian physicist.
Douglas Messerli is an American writer, professor, and publisher based in Los Angeles, California. In 1976, he started Sun & Moon, a magazine of art and literature, which became Sun & Moon press, and later Green Integer press. He has taught at Temple University in Philadelphia, and Otis College of Art and Design in Los Angeles.
The INTEGER Millennium House is a demonstration house in Watford, England that opened to the public in 1998. It was renamed The Smart Home after being refurbished in 2013. The house was originally intended to showcase innovations in design and construction, building intelligence, and environmental performance. The INTEGER design included many innovative features, including environmental technology such as a green roof and a grey water recycling system, home automation that included a building management system and an intelligent security system, and innovative technical systems such as under-floor trench heating. In 2013, the house was refurbished and retrofitted with a variety of new and upgraded features, including a building-integrated photovoltaic (BIPV) array, which altogether halved its carbon emissions and increased its energy efficiency by 50%. Since its creation, the house has garnered numerous awards, appeared on Tomorrow's World on BBC Television, hosted thousands of visitors, and influenced mainstream construction.
Los Angeles, USA