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Names of large numbers
Names of large numbers are the English words for powers of ten beyond a thousand, coined from Latin with the -illion ending, as in million, billion, and trillion.
NAND logic
NAND logic is the construction of Boolean functions and circuits using only the NAND operation, "not both", which can express every other Boolean function, making it a universal gate.
Napier's bones
Napier's bones, also called Napier's rods, are numbered calculating rods described by Scottish mathematician John Napier in 1617, designed to reduce multiplication and division to simple addition.
Narayana number
The Narayana numbers, named for the Canadian mathematician T. V. Narayana, form a symmetric triangular array counting Dyck paths with k peaks; row sums give the Catalan numbers.
Narcissistic number
A narcissistic number, also called an Armstrong number, is a number equal to the sum of its digits each raised to the number of digits, like 153.
Natural number
A natural number, or positive integer, is one of the numbers 0, 1, 2, 3, and so on, depending on convention, used for counting and ordering.
Natural transformation
A natural transformation, also called a morphism of functors, assigns to each object a morphism between two parallel functors' values, compatible with every morphism of the source category.
Near-ring
A near-ring is an algebraic structure with addition and multiplication in which addition forms a possibly nonabelian group and multiplication distributes over addition from one side only.
Negabinary
Negabinary is a positional numeral system with base −2, using digits 0 and 1, in which every positive and negative integer has a unique sign-free representation.
Negative number
A negative number, also called a directed number, is a real number less than zero; Brahmagupta gave early rules in 628, though Western acceptance came only in the 19th century.
Néron model
The Néron model, or Néron minimal model, is a smooth group scheme extending an abelian variety so every rational point extends, introduced by André Néron in 1964.
Nest algebra
A nest algebra is the algebra of bounded operators on a Hilbert space leaving invariant every subspace in a nest, a totally ordered collection of closed subspaces.
Nested intervals
Nested intervals are intervals of the real line, each containing the next; the nested interval property says closed, bounded nested intervals share a common point.
Newton's identities
Newton's identities, also called the Newton–Girard identities, are relations expressing the power sums of variables in terms of elementary symmetric polynomials, first published by Newton in 1707.
Nichols algebra
A Nichols algebra is a braided Hopf algebra generated by a braided vector space, introduced by Warren D. Nichols in 1978 as the braided analog of a symmetric algebra.
Nicolas Fatio de Duillier
Nicolas Fatio de Duillier, also known as Nicolas Fatio, was a Swiss mathematician and natural philosopher, a friend of Isaac Newton who proposed a corpuscular theory of gravity in 1690.
Nicolo Tartaglia
Nicolo Tartaglia, born Niccolo Fontana, was an Italian mathematician and engineer who solved a class of cubic equations and wrote the first printed treatise on ballistics.
Niels Henrik Abel
Niels Henrik Abel (1802–1829) was a Norwegian mathematician who proved the general fifth-degree equation cannot be solved by radicals, founded elliptic function theory, and died of tuberculosis at 26.
Nilpotent element
A nilpotent element of a ring is an element x whose some power x raised to n equals 0, making every nilpotent a zero divisor though not conversely, as with 2 in the integers mod 6.
Nilpotent group
A nilpotent group is a group whose lower central series, built by repeatedly taking commutators, reaches the trivial subgroup after finitely many steps; class 1 groups are exactly abelian.
Nilpotent Lie algebra
A nilpotent Lie algebra is a Lie algebra in which all iterated brackets of sufficient length equal zero, so it is nearly abelian and underlies nilpotent Lie groups.
Nilpotent matrix
A nilpotent matrix, or nilpotent transformation, is a square matrix for which some finite power is the zero matrix, and 0 is its only eigenvalue.
Nilradical
The nilradical of a commutative ring is the ideal of all nilpotent elements, also equal to the intersection of all prime ideals of the ring.
Nimber
A nimber, also called a Grundy value or nim-value, is the value assigned to a position in an impartial combinatorial game; a nonzero nimber means a winning position.
Noether normalization lemma
The Noether normalization lemma, a result in commutative algebra proved by Emmy Noether in 1926, states that every finitely generated algebra over a field is a finite extension of a polynomial subring.
Noetherian ring
A Noetherian ring is a ring in which every ideal can be generated by finitely many elements, named after Emmy Noether, who studied them in 1921.
Non-associative algebra
A non-associative algebra is an algebra over a field whose multiplication need not satisfy x(yz) = (xy)z; Lie, Jordan, and alternative algebras are the best-known examples.
Non-linear least squares
Non-linear least squares is a parameter estimation method that fits models nonlinear in their parameters by minimizing squared residuals, typically with the Gauss-Newton or Levenberg-Marquardt algorithm.
Non-negative matrix factorization
Non-negative matrix factorization (NMF) is a family of algorithms approximating a nonnegative matrix as a product of two lower-rank nonnegative matrices, giving additive, parts-based representations of data.
Non-standard model of arithmetic
The non-standard model of arithmetic, or non-standard arithmetic, is a model of Peano Arithmetic not isomorphic to the natural numbers, containing infinite integers, first constructed by Thoralf Skolem in 1934.