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Topic: Set builder notation

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	PlanetMath: set
		Sets can be of “real” objects or mathematical objects, but the sets themselves are purely conceptual.
		The set of all subsets of a set
		However, not every collection has to be a set (in fact, all collections can't be sets: there is no set of all sets or of all ordinals for example).
	planetmath.org /encyclopedia/Set.html (984 words)

	Real Number System - Set Notation (Site not responding. Last check: 2007-10-20)
		Conventionally, the pair of set braces, { }, are used to enclose the elements (or description thereof) of a set, using commas to separate the individual elements.
		B, is the set of all elements that are contained in sets A, B or both.
		Using this notation, a set is often defined as the collection of real numbers that belong to either an open, closed, half-open, or infinite interval (of real numbers).
	library.thinkquest.org /10030/2setnot.htm (575 words)

	Set Description Notation (Site not responding. Last check: 2007-10-20)
		Consider the set of rational numbers, which are numbers that can be expressed as a/b, where a is an integer and b is a non-zero integer.
		Infinite set in roster notation: {1, 2, 3,...} is the set of positive integers.
		The set of all numbers greater than a, where a is a real number, is represented by a darker line with a hollow point at a, and dark arrow to indicate that the set continues forever:
	mcraefamily.com /MathHelp/BasicSetDescription.htm (516 words)

	1
		Sets can be specified by a rule of formation, by listing the elements, or by set builder notation.
		We write the symbols A Í B instead of writing “set A is a subset of set B.” The symbol Í means “is a subset of” and includes the possibility of A and B being equal.
		Intersection: Denoted A Ç B, consists of the elements that are in set A and in set B.
	faculty.mdc.edu /cgil/Sets.htm (2055 words)

	Set Notation
		Sets are "unordered", which means that the things in the set do not have to be listed in any particular order.
		This is pronounced as "the set of all
		If two sets are being combined, this is called the "union" of the sets, and is indicated by a large U-type character.
	www.purplemath.com /modules/setnotn.htm (732 words)

	Section 1.2 Lesson, Math 101 - Fall 1997
		A set, B, is a subset set of a set, C, if all the elements in B are also in C. C is read "B is a subset of C."
		A set, B, is not a subset set of a set, C, if one of the elements in B is not in C. C is read "B is not a subset of C."
		Set builder notation is a way to express sets with out listing each element separately in roster form.
	www.sci.wsu.edu /~kentler/Fall97_101/nojs/Chapter1/section2.html (339 words)

	Introduction to Sets
		Set - George Cantor's definition of a set- A set is the result of collecting together certain well-determined objects of our perception or our thinking into a single whole; these objects are called the elements of the set.
		Further the empty set is a proper subset of every set except the empty set.
		This mathematical notation states the rules/clauses that are used to define the set.
	instruction.blackhawk.tec.wi.us /jbellman/sets_intro.htm (416 words)

	Set-builder notation - Wikipedia, the free encyclopedia
		In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy.
		Set builder notation binds the variable x and must be used with the same care applied to variables bound by quantifiers.
		In axiomatic set theory, this set is guaranteed to exist by the axiom schema of replacement.
	en.wikipedia.org /wiki/Set-builder_notation (800 words)

	SingaporeMoms - Parenting Encyclopedia - Set
		Sets are one of the most important and fundamental concepts in modern mathematics.
		Basic set theory, having only been invented at the end of the 19th century, is now a ubiquitous part of mathematics education, being introduced as early as elementary school.
		This set includes all rational numbers, together with all irrational numbers (that is, numbers which can't be rewritten as fractions, such as π, –π and √2).
	www.singaporemoms.com /parenting/Set (1382 words)

	Sets (Site not responding. Last check: 2007-10-20)
		Topology is an introduction to the basic definitions of terms in the study of metric sets.
		Two sets S and T are equal just when, for any x, (x is a member of S) is logically equivalent to (x is a member of T).
		Sets can be constructed by giving a property which their elements must satisfy.
	mcraefamily.com /MathHelp/BasicSet.htm (600 words)

	setth.html
		1.8 P(A) denotes the set of all subsets of a set A.
		In the first column the sets are represented by their properties as in (b), while in the second column they are expressed in terms of their elements, as in (a).
		of a set A is a set consisting of all elements of W that are not in A. 7.1 From the definition it follows that:
	www.marlboro.edu /academics/study/mathematics/courses/setth (875 words)

	Chapter 2 (Site not responding. Last check: 2007-10-20)
		The null set, represented by the symbol Æ, denotes the set consisting of no elements and is known as the empty set.
		The notation {1, 2, 3} is roster notation that describes the set A. Whenever there are a very large number of elements in a set, either the roster method cannot be used or it is very difficult to use it.
		This notation is read “All x such that x is greater than 0 and x is a real number.” In set builder notation, that which follows the colon is describing a property that an element must possess in order to be an element of the set.
	www.faculty.sfasu.edu /cproctor/1101chapter2.html (2785 words)

	Set Theory
		Set theory is also defined in terms of logic they are inextricably entwined for instance A intersect B = {x:x elem A ^ x elem B}.
		Logic and sets are closely related, and the former is a prerequisite for the latter.
		In the same sense, arithmetic and sets are related, to the point where the former is usually defined completely in terms of the latter.
	www.c2.com /cgi/wiki?SetTheory (1218 words)

	1A Set Terminology
		In the study of sets, the rules are that we have sets and we have elements, and that given any particular set and any particular element, either the element belongs to the set or it does not.
		Other disjoint pairs of sets are A and E, B and D, D and E. All other pairs of sets intersect; for example, A and C intersect because they have in common the element 3, while B and F intersect because they have in common the two elements 4 and 6.
		The sets M and F are disjoint from one another, as are the pairs F and L, W and H, and F and H (unless you believe in mermaids).
	www2.hawaii.edu /~hile/setsa.htm (1948 words)

	Set - Wikipedia, the free encyclopedia
		The study of the structure of possible sets, set theory, is quite rich and ongoing.
		Set theory, having only been invented at the end of the 19th century, is now a ubiquitous part of mathematics education, being introduced as early as primary school in many countries.
		denotes the set of all rational numbers (that is, the set of all proper and improper fractions).
	en.wikipedia.org /wiki/Set (1376 words)

	Set Theory
		are not since the former set is a set of four objects, while the latter set is a set with only three objects, one of which itself is a set.
		Note that the empty set is a member of the universal set; it is also a subset of the universal set.
		This is read as "the set of all pairs {a, b} such that a is an element of the set A and b is an element of the set B".
	www.rwc.uc.edu /koehler/comath/26.html (1557 words)

	Notation and Terminology
		The use of the word ``set'' means that there is also a method to determine whether or not a particular object belongs in the set.
		As seen above, a set could be described with a phrase such as ``the integers 1 through 5'' and the speaker hopes that it is understood.
		Finally, the complement of a set consists of those objects that are not in the given set.
	www.math.csusb.edu /notes/sets/node1.html (453 words)

	Set Theoery - Terms and Symbols
		Note that { } is different from the number "0" and the sets { 0 } and { Ø }.
		B" and "A = B" mean that the sets A and B have precisely the same elements (as well as the same size).
		A" means that "x is a member of the set A" or "x is an element of the set A".
	math.uww.edu /faculty/mcfarlat/setterms.htm (292 words)

	Set Theory
		The concepts of sets and set theory is of fundamental importance to the study of mathematics and technology applications, especially in the area of data base structures.
		Two sets are equal if and only if they contain exactly the same elements, regardless of the order of the elements.
		The cardinal number of set A, is symbolically represented by n(A), and is read "n of A." Two sets are equivalent if their cardinal numbers are equal.
	instruction.blackhawk.tec.wi.us /jbellman/sets.htm (344 words)

	IS 2000
		This type of notation is called set builder notation and it is the preferred way of describing sets.
		Set A is a subset of B, denoted A
		If a set S has a finite number of elements, S is the finite set with n elements.
	www.sis.pitt.edu /~logicp/group3/setVocab.html (456 words)

	Intermediate Algebra Tutorial on Sets of Numbers
		It is important to know set builder notation, especially in mathematics, because it allows you to group together large number of elements that belong to a certain category.
		However, if your set has hundreds or thousands of elements, it would be hard to list them out, but easy to refer to them using set builder notation.
		The only difference between this set and the one above is that this set not only contains all the natural numbers, but it also contains 0, where as 0 is not an element of the set of natural numbers.
	www.wtamu.edu /academic/anns/mps/math/mathlab/int_algebra/int_alg_tut3_sets.htm (2268 words)

	[No title]
		The set of negative integers between -5 and 7¡+©Ôó ¨Empty Set (Page 52)¡4 0ÿþ ÿþ0ÿþ¨ÚThe empty set, or null set, is the set that contains no elements.
		As an example of the empty set, consider the set of natural numbers that are negative integers.
		For instance, in set-builder notation, the set of natural numbers greater than 7 is written as follows.
	math.indstate.edu /chi/ma102/section2_1.ppt (1380 words)

	6
		Set builder notation—the elements are described by requirements they must fill.
		A is also true because the set {1} is not in the list of elements of A. The empty set is the set with no elements denoted by zero with a line through it.
		B} is the intersection of A and B. The intersection is the set of
	www.math.tamu.edu /~jlewis/Sets.htm (1753 words)

	An Elementary Introduction to Logic and Set Theory: Set Theory
		The intersection of two sets is the "overlap", i.e., the part of the two sets which is common to both.
		Often we are interested in relationships between two sets of objects in which the choice of an object in one set completely and unambiguously determines the related object in the second set.
		Specifically, he considered the set of all sets that are not elements of themselves, i.e., the set of all collections that are not self-contained.
	matcmadison.edu /alehnen/weblogic/logset.htm (8279 words)

	[No title]
		I - the set of all integers ------------------------------ I = {..., -3, -2, -1, 0, 1, 2, 3,...} (Note: "..." is the ellipses which in this context means "continue in like manner in the appropriate direction").
		I+ - the set of all positive integers ---------------------------------------- I+ = { 1, 2, 3,...} We will consider 0 to be neither positive nor negative, so we won't include it in this set.
		H - Set of Hexadecimal Numbers --------------------------------- H = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, A, B, C, D, E, F } 6.
	www.unf.edu /public/cot3100/jgiles/lecture1 (1420 words)

	2.6 Class Notes
		One way to write the solution of an inequality in one variable is to use interval notation.
		In interval notation we use parentheses ()and brackets [ ].
		Graph and write the solution in interval and set-builder notation.
	mtsu32.mtsu.edu:11197 /2_6_class_notes.htm (207 words)

	BioMath: Mathematical Notation
		Set-builder notation is commonly used to compactly represent a set of numbers.
		We can use set-builder notation to express the domain or range of a function.
		Interval notation can be used to express a variety of different sets of numbers.
	www.biology.arizona.edu /BioMath/tutorials/Notation/SetBuilderNotation.html (304 words)

	Solving Linear Inequalities (one variable)
		The union of a set A and set B, written
		, is the set of elements that belong to either set A or set B. The intersection of a set A and set B, written
		, is the set of elements that are common to both set A and set B. Given set A and B, find
	www.math.utep.edu /Student/alfredo/0311/101.htm (133 words)

	Using Interval Notation
		To be able to view the math in this document, use the PDF version, or please consider using another browser, such as Mozilla, Netscape 7 or above or Microsoft Internet Explorer 6 or above (MathPlayer required for IE).
		Interval notation is another method for writing domain and range.
		In set builder notation braces (curly parentheses {}) and variables are used to express the domain and range.
	cnx.org /content/m13596/latest (257 words)

	[No title]
		For the relation R on the set X, where X={1,2,3,4} and R={(1,1), (2,2), (3,3), (4,4)}, the relation R is reflexive.
		Also, A set of all people containing pairs of people {(Bob, Sally), (Frank,Joe), (Ann,Susan)} where each pair shares the same mother and father is reflexive.
		For the relation R on the set X, where X={1,2,3,4} and R={(1,3), (3,1),(3,2),(2,3)}, the relation R is symmetric.
	www.personal.psu.edu /pld2/ist230fall01/SetFunctionNotes.ppt (490 words)

	Section4_1 (Site not responding. Last check: 2007-10-20)
		1) Rewrite the following inequalities in both set builder notation and interval notation.
		2) For the following graphs write the interval notation and the set builder notation.
		4) Solve the following graphs and write the interval notation as well as the set builder notation.
	web.pdx.edu /~bragstad/95/Section4_1.html (103 words)

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