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		secant – singular cardinal secant   Geometry: A line connecting two points on a curve. Trigonometry: A periodic trigonometric function defined on angles, usually abbreviated “sec.” It is the multiplicative inverse of the cosine function. See the related article for a complete exposition. Related article: Trig Functions and Identities semi-finite measure   See measure. semigroup   See group. semi-lattice   A set with a single binary operation that is idempotent, commutative, and associative. Cf. lattice. sentential calculus   See propositional calculus. separable   A topological space is separable if it has a countable base. sequence   A sequence is a set (of numbers, or sets, or functions, etc.) indexed by the natural numbers. Sequences may be infinite, and may be regarded as a function with domain the set of natural numbers and range the set of objects in the sequence. An infinite sequence of numbers is said to converge to a number L provided that, given any positive e, we may find a natural number N such that for all terms of the sequence after the N th one, their difference from L is less than e. Naively, the terms of the sequence eventually become “arbitrarily close” to L. Such a sequence is called convergent, and the number L is called the limit of the sequence, or the limit point, or sometimes the accumulation point of the sequence. Alternatively, a cluster point or accumulation point P of a sequence may be defined as a point with the property that infinitely many terms of the sequence lie in any neighborhood of P. A sequence may have more than one such cluster point (even infinitely many). A sequence is called Cauchy if, for every e greater than zero, we may find a natural number N so that the difference between any two terms following the N th term is smaller than e. Every convergent sequence is Cauchy; the converse is true in complete spaces. Cf. series. Related article: Limits series    ARTICLE   A series is an infinite sum, where the nth summand is the nth term of a sequence. A series is usually denoted using “sigma notation,” i.e., The index n may begin with 0, 1, or k for any natural number k, as a matter of convenience. The nth partial sum Sn of a series is the (finite) sum of the first n terms of the series. A series is said to converge if and only if its sequence of partial sums {S 1, S 2, . . . , Sn, . . . } is a convergent sequence. There are several important types of series and several tests for the convergence of a series. Additionally, most useful functions have Taylor series representations, which makes them very important in the study of differential equations. See the article for a complete description. set   Naively, any well-defined collection considered as a single, abstract object. By “well-defined” is meant that it is always possible to determine for a given set when something is an element of the set and when not. In formal set theory, the term “set” is not defined, but is a primitive term whose meaning is informed purely by the axioms in which it appears. Cf. ZF, ZFC. set algebra   See algebra of sets. set difference   The set difference of two sets A and B, denoted A - B or A \ B, is the set of elements that is contained in A but not in B. This is equivalent to the intersection between A and the complement of B. set function   A function whose domain of definition is a collection of sets. set ring   See ring of sets. set theory   Naive set theory: The study of sets (i.e., well-defined collections of objects) which have a binary extensional relation (set membership) defined on them. Abstract set theory: As naive set theory, but with all sets built using only elements which are themselves sets (beginning with the empty set, which has no members). Formal set theory: Any of several axiom systems of abstract set theory in the language of first-order logic, such as Zermelo Fraenkel set theory, Gödel-Bernays set theory, Quine’s New Foundations, etc. Sid’s Paradox    ARTICLE   A paradox of knowledge: is the distinction between matters of opinion and matters of fact a matter of opinion or a matter of fact? See the article for discussion. signed measure   Given a set X together with a s-algebra of sets M defined on it, a signed measure on (X, M) is an extended real-valued function m with domain M satisfying: The signed measure of the empty set is zero. The signed measure m assumes at most one of the values +/- infinity. (Countable additivity) Given a countable sequence of disjoint sets in M, the signed measure of the union of the sequence is equal to the sum of the signed measures of the sets in the sequence, where this sum converges absolutely if the signed measure of the union is finite. Technically speaking, every measure is a signed measure; ordinary (i.e., nowhere negative) measures are sometimes called positive measures. similar   Graph Theory: Two vertices or edges of a graph are called similar if there is an automorphism of the graph that takes one to the other. sin   See sine. sine    ARTICLE   A periodic trigonometric function defined on angles. Usually abbreviated “sin.” See the article for a complete exposition. Cf. tangent, cosine. singleton set   A set with exactly one element. singular cardinal   A cardinal that is not regular.
		secant – singular cardinal

HOME | ABOUT | CONTACT | AD INFO | PRIVACY Copyright © 1997-2013, Math Academy Online™ / Platonic Realms™. Except where otherwise prohibited, material on this site may be printed for personal classroom use without permission by students and instructors for non-profit, educational purposes only. All other reproduction in whole or in part, including electronic reproduction or redistribution, for any purpose, except by express written agreement is strictly prohibited. Please send comments, corrections, and enquiries using our contact page.