Sets in math

• [PDF File]Set Theory - UCLA Mathematics

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  All sets are arranged into a cumulative hierarchy. We begin with a simple collection of sets, and then apply some basic operations to iteratively create more sets. This produces the hierarchy V of all sets. The precise set existence axioms we will use will be discussed in the next section. They are known as Zermelo-Frankel set theory or ZF. We ...

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• [PDF File]SETs and Anti-SETs: The Math Behind the Game of SET

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  SETs and Anti-SETs: The Math Behind the Game of SET Charlotte Chan 19 July 2010 In this paper, we will use the above change in font to distinguish between the English word \set" and a SET in the sense of the game. This way, we will be able to easily distinguish between, say SET theory and set theory, where the former means the math behind the game

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• [PDF File]Countable and Uncountable Sets - Brown University

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  Countable and Uncountable Sets Rich Schwartz November 12, 2007 The purpose of this handout is to explain the notions of countable and uncountable sets. 1 Basic Definitions A map f between sets S1 and S2 is called a bijection if f is one-to-one and onto. In other words • If f(a) = f(b) then a = b. This holds for all a,b ∈ S1.

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• [PDF File]Addition and multiplication of sets - City University of ...

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  Math. Log. Quart. 53, No. 1, 52–65 (2007) / DOI 10.1002/malq.200610026 Addition and multiplication of sets Laurence Kirby∗ Department of Mathematics, Baruch College, City University of New York,

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• [PDF File]Introduction to Sets and Functions - Florida State University

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  1. INTRODUCTION TO SETS 13 Definition 1.7.2. The intersection of sets Aand B, denoted by A\B(read \Aintersection B"), is the set consisting of all elements that belong both Aand B. In symbols A\B= fxjx2Aand x2Bg Definition 1.7.3. The di erence or relative compliment of two sets Aand B, denoted by A Bis the set of all elements in Athat are not in B.

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• [PDF File]Sets and set operations - University of Pittsburgh

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  4 CS 441 Discrete mathematics for CS M. Hauskrecht Equality Definition: Two sets are equal if and only if they have the same elements. Example: • {1,2,3} = {3,1,2} = {1,2,1,3,2} Note: Duplicates don't contribute anythi ng new to a set, so remove them. The order of the elements in a set doesn't contribute

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• [PDF File]Basic Set Theory - UH

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  We now move on to a number of operations on sets. You are already familiar with several operations on numbers such as addition, multiplication, and nega-tion. Definition 2.5 The intersection of two sets S and T is the collection of all objects that are in both sets. It is written S ∩ T. Using curly brace notation S ∩ T = {x : (x ∈ S) and ...

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• [PDF File]GRADE 7 MATH LEARNING GUIDE Lesson I: SETS: AN ...

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  GRADE 7 MATH LEARNING GUIDE Lesson I: SETS: AN INTRODUCTION Time: 1.5 hours Pre-requisite Concepts: Whole numbers About the Lesson: This is an introductory lesson on sets. A clear understanding of the concepts in this lesson will help you easily grasp number properties and enable you to quickly identify multiple solutions involving sets of numbers.

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• [PDF File]Sets and Functions

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  1.1. Sets A set is a collection of objects, called the elements or members of the set. The objects could be anything (planets, squirrels, characters in Shakespeare’s plays, or other sets) but for us they will be mathematical objects such as numbers, or sets of numbers. We write x2Xif xis an element of the set Xand x=2Xif xis not an element of X.

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• [PDF File]Proofs Involving Sets - Gordon College

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  MAT231 (Transition to Higher Math) Proofs Involving Sets Fall 2014 10 / 11. Example A Proposition fp : p is a prime numberg\fk2 1 : k 2Ng= f3g. Proof. Let x 2fp : p is a prime numberg\fk2 1 : k 2Ng so that x is prime and x = k2 1 = (k 1)(k + 1). This shows that x has two factors.

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• [PDF File]Math 211 Sets Practice Worksheet--Answers

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  Math 211 Sets Practice Worksheet--Answers 4. Refer to the diagram to answer the questions below. i) Only Region 1 is shaded. ii) Only Region 7 is shaded.

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• [PDF File]Set (mathematics)

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  Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a

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• [PDF File]SETS AND SET NOTATION - Texas A&M University

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  A = fxjx is a female in math 166 this semesterg: A UNIVERSAL SET is a set from which all the member of the sets in a problem can be drawn. U = fxjx is a student in math 166 this semesterg We use VENN DIAGRAMS to show sets. The rectangle is the universal set and the circles are sets in the universal set. AsetCis a subset of A if every element in ...

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• [PDF File]Discrete Maths: Exercises and Solutions

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  Sets are used extensively in counting problems, and for such applications we need to discuss the sizes of sets. Definition: Let S be a set. If there are exactly n distinct elements in S where n is a nonnegative integer, we say that S is a finite set and that n is the cardinality of S.

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• [PDF File]AN INTRODUCTION TO SET THEORY - University of Toronto ...

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  statements about sets and functions. They look like they could appear on a homework assignment in an undergraduate course. 1. For any two sets X and Y, either there is a one-to-one function from X into Y or a one-to-one function from Y into X. 2. If there is a one-to-one function from X into Y and also a one-to-one

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• [PDF File]Math 127: Set Theory

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  Math 127: Set Theory Mary Radcli e 1 Basics We begin these notes on set theory with a de nition of a set, and the basic notation we use to represent sets. De nition 1. A set X is a collection of elements from a known universe . We have seen sets crop up here and there before. In discussion variables used in propositional formulae,

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• [PDF File]Sets, Functions, Relations - NU Math Sites

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  Sets, Functions, Relations 2.1. Set Theory 2.1.1. Sets. A set is a collection of objects, called elements of the set. A set can be represented by listing its elements between braces: A = {1,2,3,4,5}. The symbol ∈ is used to express that an element is (or belongs to) a set, for instance 3 ∈ A. Its negation is represented by 6∈, e.g. 7 6∈ ...

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• [PDF File]Sets & Numbers - Math

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  Among the most common sets appearing in math are sets of numbers. There are many di↵erent kinds of numbers. Below is a list of those that are most important for this course. Natural numbers. N = {1,2,3,4,...} Integers. Z = {...,2,1,0,1,2,3,...} Rational numbers. Q is the set of fractions of integers. That is, the

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