BROWSE ALPHABETICALLY LEVEL:    Elementary    Advanced    Both INCLUDE TOPICS:    Basic Math    Algebra    Analysis    Biography    Calculus    Comp Sci    Discrete    Economics    Foundations    Geometry    Graph Thry    History    Number Thry    Phys Sci    Statistics    Topology    Trigonometry monomorphism – octahedron monomorphism   A morphism f from X to Y is called a monomorphism when it is injective, that is, when to each element y of Y there corresponds at most one x in X such that f(x) = y.Cf. epimorphism. monotone function   Also called monotonic function. See order-preserving function. morphism   A function from one set to another is called a morphism if it preserves some designated structural properties or operations on the domain set. Typically, the word morphism is not used by itself, but in combination with a prefix that indicates whether it is injective, surjective, etc.Cf. automorphism, epimorphism, homeomorphsim, homomorphism, isomorphism, monomorphsim. multiplication   A binary operation on numbers or quantities resulting in a product, usually but not always amounting to repeated addition. On the natural numbers multiplication is defined recursively by the Peano axioms, such that the product of two numbers n and m, denoted by n × m, is found by adding up m copies of n (or n copies of m).Multiplication of most kinds of numbers is associative and commutative, but these properties sometimes fail, for example in the case of matrix multiplication.When a product of more than two numbers or quantities is taken, the general product may be denoted by the capital Greek letter Pi, i.e., Pai denotes the product a1 × a2 × . . . × an. multiply   To find the product of two numbers or quantities by multiplication. mutually prime   Two integers are mutually prime if they have no common factors larger than 1 or -1. natural base   See Euler number. natural logarithm   A logarithm with base e, the Euler number. Often written “ln” rather than “log” to distinguish it from logarithms using other bases. natural number   An element of the set N = {1, 2, 3, ...} consisting of all the “counting numbers.” When the number 0 is included, this set is sometimes called the whole numbers. In set theory, the natural numbers (incuding 0) are identified with the set w of finite ordinals. The natural numbers are a well-founded linear order with no largest member, and are countably infinite.Cf. Peano axioms, rational number, real number. Related MiniText: Number -- What Is How Many? negation   If j is a statement, sentence, or formula of logic, then the negation of j, denoted by j, is that formula which is true whenever j is false, and false whenever j is true. negative   The negative of a number or quantity x is the number, denoted -x, which when added to x yields 0. That is, the negative of a number is its additive inverse. non-denumerable   norm   Analysis: A non-negative real-valued function “|| x ||” defined on a vector space, satisfying|| –x || = || x ||,|| cx || = || c || × || x || for all scalars c, and|| x + y || <= || x || + || y || (triangle inequality)Statistics: Another term for the mode of a frequency distribution. normal   A line intersecting a curve (or surface) perpendicular to the tangent line (or tangent plane) at the point of intersection. The normal to a surface expressed as a function of several variables xi is given by the gradient. normal subgroup   See subgroup. normed space   A vector space with a norm defined on it. nowhere dense   Given a space X and a subset A of X, we say that A is nowhere dense if every open set of X contains an open subset that is disjoint from A. This is equivalent to saying that the complement of A is dense, or that A has empty interior. number   There is no precise mathematical definition of the word “number.” There are however precise definitions of the terms “natural number,” “rational number,” “real number,” “complex number,” and other less commonly used kinds of number. When a mathematician speaks about numbers she usually has one of these cases in mind and she should, at the outset, make it clear to which type of number she is referring. The naive, inborn concept of number that is shared to some degree by all humans is a matter for philosophical rather than strictly mathematical inquiry, and it may be noted that there has historically been strong opposition to the introduction of new generalizations of established concepts of number. numeral   Graphical symbol representing a number. obtuse   An angle is called obtuse if it is greater than a right angle, that is, if its measure is greater than 90° (p/2 radians). A triangle is called obtuse if one of its angles is obtuse.Cf. acute. octahedron   A polyhedron having eight faces.The faces of a regular octahedron are congruent, equilateral triangles.Cf. Platonic solid, polyhedron. monomorphism – octahedron
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