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Cardinality of the continuum
The cardinality of the continuum, also called the power of the continuum, is the size of the set of real numbers, strictly larger than that of the natural numbers.
Cardioid
A cardioid is a heart-shaped plane curve traced by a point on a circle rolling around a fixed circle of equal radius, used as the pick-up pattern of many microphones.
Carl Friedrich Gauss
Carl Friedrich Gauss (1777–1855) was a German mathematician and astronomer called the Prince of Mathematicians, whose 1801 Disquisitiones Arithmeticae made number theory a systematic subject.
Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi, also known as Carl Jacobi, was a German mathematician (1804–1851) known for elliptic functions, the Jacobian, and the Hamilton–Jacobi theory in analytical mechanics.
Carmichael function
The Carmichael function λ(n), also called the reduced totient function, is the least positive exponent m such that a^m ≡ 1 (mod n) for every a coprime to n.
Carmichael number
A Carmichael number, also called an absolute pseudoprime, is a composite number that satisfies Fermat's little theorem for every base coprime to it, defeating the Fermat primality test.
Carry-lookahead adder
The carry-lookahead adder (CLA), also known as a fast adder, is a digital circuit that adds binary numbers by computing every carry in parallel instead of rippling, introduced in 1958.
Cartan connection
The Cartan connection is a Lie-algebra-valued 1-form on a principal bundle, due to Élie Cartan, that describes a curved manifold by comparing it with a model geometry.
Cartan decomposition
The Cartan decomposition is a structural decomposition of a real semisimple Lie algebra into the eigenspaces of the Cartan involution, underlying the theory of symmetric spaces.
Cartan matrix
A Cartan matrix is an integer square matrix encoding the angles and relative lengths of a root system's simple roots, determining its Lie algebra and Dynkin diagram.
Cartan subalgebra
A Cartan subalgebra is a maximal abelian subalgebra of a semisimple Lie algebra whose elements act diagonally; fixing one yields the root space decomposition underlying the classification of semisimple Lie algebras.
Cartesian closed category
A cartesian closed category is a category with finite products and, for each pair of objects, an exponential object B^A behaving like a function space, as in the category of sets.
Cartesian coordinate system
The Cartesian coordinate system, also called rectangular coordinates, locates points in the plane by ordered pairs of distances from fixed perpendicular axes, and is named after René Descartes.
Cartesian product
The Cartesian product of two sets A and B, written A × B, is the set of all ordered pairs (a, b) with a in A and b in B.
Casimir element
The Casimir element, also known as the Casimir operator or Casimir invariant, is a central element of a Lie algebra's universal enveloping algebra, named for Hendrik Casimir.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an integer invariant of a coherent sheaf on projective space, or of a graded module, measuring the twist at which higher cohomology vanishes; introduced by David Mumford in 1966.
Catalan number
The Catalan numbers, also called the Catalan sequence, form an integer sequence beginning 1, 1, 2, 5, 14, 42 that counts balanced parentheses and triangulations.
Catalan numbers
The Catalan numbers are the integer sequence beginning 1, 1, 2, 5, 14, 42, counted by Euler in 1751, that enumerates balanced parentheses, binary trees, and polygon triangulations.
Catastrophic cancellation
Catastrophic cancellation is the loss of significant digits that occurs when two nearly equal numbers are subtracted, inherent to approximations rather than floating point itself, and fixed by algebraic rewriting.
Catch-22 (logic)
The Catch-22 problem is a situation in which a desired outcome is impossible to attain because of inherently contradictory rules, coined by Joseph Heller in his 1961 novel.
Categorical distribution
The categorical distribution, also called the multinoulli distribution, is the discrete probability distribution of a single draw landing in one of k categories, each with a specified probability.
Categorical logic
Categorical logic is the study of logic using category theory, interpreting logical systems as objects and morphisms in categories and unifying syntax, semantics, and proof theory.
Categorical variable
A categorical variable, also called a qualitative variable, takes values from a limited set of categories describing a characteristic, such as blood type or diagnosis, rather than a measurable quantity.
Categoricity
Categoricity is the model-theoretic property that a theory has exactly one model of a given cardinality up to isomorphism; Morley's 1965 theorem made it central.
Categorification
Categorification is a mathematical technique that replaces set-theoretic notions with category-theoretic analogs: sets become categories, functions become functors, and equations become natural isomorphisms between functors.
Category (mathematics)
In mathematics, a category is a structure consisting of objects together with morphisms between them, with identity morphisms and associative composition, introduced by Eilenberg and Mac Lane in 1945.
Category theory
Category theory is a branch of abstract algebra that studies mathematical structures through morphisms between objects. Eilenberg and Mac Lane introduced it in the 1940s.
Catenary
The catenary, also called the catenary curve, is the curve a hanging chain or cable assumes under its own weight; Leibniz, Huygens, and Johann Bernoulli derived its equation in 1691.
Catmull–Rom spline
A Catmull–Rom spline is a family of cubic interpolating splines introduced by Edwin Catmull and Raphael Rom in 1974, and a standard tool in computer graphics, animation, and path planning.
Cauchy distribution
The Cauchy distribution, also known as the Lorentz distribution, is a continuous probability distribution that resembles the normal distribution but has heavier tails, so its mean and variance do not exist.