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Subset In mathematics , especially in set theory , a set A is a SUBSET of a set B, or equivalently B is a SUPERSET of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called INCLUSION or sometimes CONTAINMENT. The subset relation defines a partial order on sets. The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion . CONTENTS * 1 Definitions * 2 Property * 3 ⊂ and ⊃ symbols * 4 Examples * 5 Other properties of inclusion * 6 See also * 7 References * 8 External links DEFINITIONSIf A and B are sets and every element of A is also an element of B, then: * A is a SUBSET of (or is included in) B, denoted by A B {displaystyle Asubseteq B} , or equivalently * B is a SUPERSET of (or includes) A, denoted by B A [...More...]  "Subset" on: Wikipedia Yahoo 

Superset (other) SUPERSET may refer to: * Superset Superset in mathematics and set theory * SuperSet Software , a group of friends who later became part of the early Novell Novell [...More...]  "Superset (other)" on: Wikipedia Yahoo 

There Exists In predicate logic , an EXISTENTIAL QUANTIFICATION is a type of quantifier , a logical constant which is interpreted as "there exists", "there is at least one", or "for some". Some sources use the term EXISTENTIALIZATION to refer to existential quantification. It is usually denoted by the turned E (∃) logical operator symbol , which, when used together with a predicate variable, is called an EXISTENTIAL QUANTIFIER ("∃x" or "∃(x)"). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. CONTENTS * 1 Basics * 2 Properties * 2.1 Negation * 2.2 Rules of Inference * 2.3 The empty set * 3 As adjoint * 4 HTML encoding of existential quantifiers * 5 See also * 6 Notes * 7 References BASICSConsider a formula that states that some natural number multiplied by itself is 25 [...More...]  "There Exists" on: Wikipedia Yahoo 

Equal (math) In mathematics , EQUALITY is a relationship between two quantities or, more generally two mathematical expressions , asserting that the quantities have the same value, or that the expressions represent the same mathematical object . The equality between A and B is written A = B, and pronounced A equals B. The symbol "=" is called an "equals sign ". Thus there are three kinds of equality, which are formalized in different ways. * Two symbols refer to the same object. * Two sets have the same elements. * Two expressions evaluate to the same value, such as a number, vector, function or set.These may be thought of as the logical, settheoretic and algebraic concepts of equality respectively [...More...]  "Equal (math)" on: Wikipedia Yahoo 

Line (mathematics) The notion of LINE or STRAIGHT LINE was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature ) with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined in this manner: "The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which will leave from its imaginary moving some vestige in length, exempt of any width [...More...]  "Line (mathematics)" on: Wikipedia Yahoo 

Order Isomorphism In the mathematical field of order theory an ORDER ISOMORPHISM is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that one of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections [...More...]  "Order Isomorphism" on: Wikipedia Yahoo 

Prime Number A PRIME NUMBER (or a PRIME) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number . For example, 5 is prime because 1 and 5 are its only positive integer factors , whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory : any integer greater than 1 is either a prime itself or can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3. The property of being prime is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division [...More...]  "Prime Number" on: Wikipedia Yahoo 

Eric W. Weisstein ERIC WOLFGANG WEISSTEIN (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science ( ScienceWorld ). He is the author of the CRC Concise Encyclopedia of Mathematics . He currently works for Wolfram Research , Inc. CONTENTS * 1 Education * 2 Career * 2.1 Academic research * 2.2 MathWorld, ScienceWorld and Wolfram Research * 2.3 Further scientific activities * 3 Footnotes * 4 References * 5 External links EDUCATION Weisstein holds a Ph.D. in planetary astronomy which he obtained from the California Institute of Technology 's (Caltech) Division of Geological and Planetary Sciences in 1996 as well as an M.S. in planetary astronomy in 1993 also from Caltech. Weisstein graduated Cum Laude from Cornell University with a B.A. in physics and a minor in astronomy in 1990 [...More...]  "Eric W. Weisstein" on: Wikipedia Yahoo 

Inequality (mathematics) In mathematics , an INEQUALITY is a relation that holds between two values when they are different (see also: equality ). * The notation a ≠ b means that a is NOT EQUAL TO b. It does not say that one is greater than the other, or even that they can be compared in size. If the values in question are elements of an ordered set , such as the integers or the real numbers , they can be compared in size. * The notation a < b means that a is LESS THAN b. * The notation a > b means that a is GREATER THAN b. In either case, a is not equal to b. These relations are known as STRICT INEQUALITIES. The notation a < b may also be read as "a is strictly less than b" [...More...]  "Inequality (mathematics)" on: Wikipedia Yahoo 

Rational Number In mathematics , a RATIONAL NUMBER is any number that can be expressed as the quotient or fraction p/q of two integers , a numerator p and a nonzero denominator q. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers, often referred to as "THE RATIONALS", the FIELD OF RATIONALS or the FIELD OF RATIONAL NUMBERS is usually denoted by a boldface Q (or blackboard bold Q {displaystyle mathbb {Q} } , Unicode ℚ); it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient ". The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10 , but also for any other integer base (e.g. binary , hexadecimal ). A real number that is not rational is called irrational [...More...]  "Rational Number" on: Wikipedia Yahoo 

International Standard Book Number The INTERNATIONAL STANDARD BOOK NUMBER (ISBN) is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an ebook , a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007. The method of assigning an ISBN is nationbased and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9digit STANDARD BOOK NUMBERING (SBN) created in 1966. The 10digit ISBN format was developed by the International Organization for Standardization (ISO) and was published in 1970 as international standard ISO 2108 (the SBN code can be converted to a ten digit ISBN by prefixing it with a zero) [...More...]  "International Standard Book Number" on: Wikipedia Yahoo 

Mathematical Reviews MATHEMATICAL REVIEWS is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics , statistics , and theoretical computer science . The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of Mathematical Reviews and additionally contains citation information for almost 3 million papers. CONTENTS * 1 Reviews * 2 Online database * 3 Mathematical citation quotient * 4 Current Mathematical Publications * 5 See also * 6 References * 7 External links REVIEWS Mathematical Reviews was founded by Otto E [...More...]  "Mathematical Reviews" on: Wikipedia Yahoo 

Isomorphic In mathematics , an ISOMORPHISM (from the Ancient Greek Ancient Greek : ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping ) that admits an inverse. Two mathematical objects are ISOMORPHIC if an isomorphism exists between them. An automorphism is an isomorphism whose source and target coincide. The interest of isomorphisms lies in the fact that two isomorphic objects cannot be distinguished by using only the properties used to define morphisms; thus isomorphic objects may be considered the same as long as one considers only these properties and their consequences. For most algebraic structures , including groups and rings , a homomorphism is an isomorphism if and only if it is bijective [...More...]  "Isomorphic" on: Wikipedia Yahoo 

MathWorld MATHWORLD is an online mathematics reference work, created and largely written by Eric W. Weisstein . It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation 's National Science Digital Library grant to the University of Illinois at Urbana–Champaign . CONTENTS * 1 History * 2 CRC lawsuit * 3 See also * 4 References * 5 External links HISTORYEric W. Weisstein, the creator of the site, was a physics and astronomy student who got into the habit of writing notes on his mathematical readings. In 1995 he put his notes online and called it "Eric's Treasure Trove of Mathematics." It contained hundreds of pages/articles, covering a wide range of mathematical topics. The site became popular as an extensive single resource on mathematics on the web. Weisstein continuously improved the notes and accepted corrections and comments from online readers [...More...]  "MathWorld" on: Wikipedia Yahoo 

McGrawHill MCGRAWHILL EDUCATION (MHE) is an American learning science company and one of the "big three" educational publishers that provides customized educational content, software, and services for preK through postgraduate education . The company also provides reference and trade publications for the medical, business, and engineering professions. McGrawHill Education currently operates in 28 countries, has more than 4,800 employees globally, and offers products and services to over 135 countries in nearly 60 languages. Formerly a division of The McGrawHill Companies , now S&P Global , McGrawHill Education was divested from McGraw Hill Financial and acquired by Apollo Global Management in March 2013 for $2.4 billion in cash [...More...]  "McGrawHill" on: Wikipedia Yahoo 

Walter Rudin WALTER RUDIN (May 2, 1921 – May 20, 2010) was an Austrian American mathematician and professor of Mathematics at the University of Wisconsin–Madison . In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis (informally referred to by students as "Baby Rudin", "Papa Rudin", and "Grandpa Rudin", respectively). Principles of Mathematical Analysis was written when Rudin was C. L. E. Moore Instructor at MIT, only two years after obtaining his Ph.D. from Duke University. Principles, acclaimed for its elegance and clarity, has since become a standard textbook for introductory real analysis courses in the United States. Rudin's analysis textbooks have also been influential in mathematical education worldwide, having been translated into 13 languages, including Russian, Chinese, and Spanish [...More...]  "Walter Rudin" on: Wikipedia Yahoo 