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 sphere – symmetric difference sphere   A closed surface, all points of which are equidistant from a given point, called the center. In 3-dimensional Euclidean space, the equation of a sphere of radius r and center (h, j, k) isThe term sphere may also refer to the solid bounded by this surface, and the interior is then called the open sphere of radius r.More generally, a sphere may be defined as the set of points in n-dimensional space (or any metric space) equidistant from a given point. The unit sphere in n-dimensional space is typically denoted S n - 1. Thus, the unit sphere in ordinary 3-space is denoted S2, and the unit circle in the plane is denoted S1. square   A regular polygon having four equal sides and four right angles. stationary set   If a is an ordinal, a set S in a is called stationary if S has non-empty intersection with every closed unbounded subset of a. Stone-Weierstrass Theorem   If X is a compact space and C(X) denotes the space of all continuous functions on X, and A is an algebra of functions in C(X) which separates the points of C(X) and which contains a constant function f not identically zero, then A is dense in C(X). story problem    ARTICLE   A mathematical problem presented as a real-world situation. See the article for problem solving techniques. subbase   In a topological space, a subbase is a collection of sets, the collection of all finite intersections of which constitutes a base. subset   A set A is a subset of a set B if every element of A is also an element of B. If in addition B is a subset of A, then A = B, but if not then A may be said to be a proper subset of B.Cf. superset. subtract   To subtract a number m from a number n is to calculate the difference of m and n. If m is less than n we take the positive difference, otherwise we take the negative of the difference. This is tantamount to adding the negative of m to n. successor   In a structure with an order relation defined upon it, the successor of an element a is the least element greater than a, if such exists.Cf. predecessor. sumset   Given a set A, the sumset of A, denoted byis the set containing all of the elements of the elements of A, that is, it is the union of the elements of A. sumset axiom   An axiom of set theory which states that if A is any set, then the sumset of A is also a set. sup   Abbreviation of supremum. superset   A set A is a superset of a set B if every element of B is an element of A.Cf. subset. supplemental angles   Two angles are supplemental if they add up to 180 degrees (p radians).Cf. complementary angles. supremum   The supremum of any subset of a linearly ordered set is the least upper bound of the subset. In particular, the supremum of any set of numbers is the smallest number in the set which is greater than or equal to every number in the set. In a complete linear order the supremum of any bounded set always exists.Cf. infimum, least upper bound axiom. surd   (rare) An irrational root of a number, e.g., the square root of two. Related article: Irrationality of the Square Root of 2 surjection   A surjective function, i.e., a function that maps at least one element of its domain to each element of its range.Cf. injection, bijection. surjective   A function f from a set X to a set Y is surjective, also called “onto,” if to each element y of Y there is an element x of X such that f maps x to y, i.e., f (x)=y. Compare: injective, bijective. Suslin tree   Set Theory: For a an infinite cardinal, an a-Suslin tree is a tree T such that |T| = a, and every chain and every antichain of T has cardinality less than a.Cf. Aronszajn tree. symbolic logic   Logic reduced to syntax, i.e., which works only with uninterpreted symbols. The two most often used kinds of symbolic logic are the propositional calculus and the predicate calculus. symmetric difference   The symmetric difference of two sets A and B is the set of those elements that are in either A or B but not both.Cf. intersection, union. sphere – symmetric difference
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