Basic properties of sets pdf

With each number, place it in the appropriate region. When two numbers are added, the sum is the same regardless of the order in which the numbers are added. Properties of union and intersection of sets the following set properties are given here in preparation for the properties for addition and multiplication in arithmetic. The properties of these sets of numbers that make them distinct are.

Set notation uses curly braces, with elements separated by commas. One of the goals of group theory is to classify all group structures on all sets in a useful way. Chapter 4 set theory nanyang technological university. Will work on this in the class, but you can find an answer at the back of the textbook. The order of the elements in a set doesnt contribute anything new. Set theory examples, body, basic, part, properties of sets. There are two methods of representing a set i roaster or tabular form ii set builder form 1. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied. A set is a collection of objects that have something in common or follow a rule. The most basic properties are that a set can have elements, and that two sets are equal one and the same if and only if every element of each set is an element of the other. In other words, we wont describe what a set is, we will describe what can be done with sets. Duplicates dont contribute anythi ng new to a set, so remove them. Basic building block for types of objects in discrete mathematics.

Using the language of sets, we say that 0 is an element of the nonnegative integers but 0 is not an element of the positive integers. The basic syntax of the exportasfixedformat method is generally as follows. The most basic properties are that a set can have elements, and that two sets are equal. Make sure this fits by entering your model number basic properties of numbers educational classroom math poster 12 x 18 poster on high quality heavy 80lb satin cover paper durable and can stand up to all kinds of abuse and it wont pucker and wrinkle like others do. Properties of set operation subjects to be learned. Stepbystep guide and 10 code examples to export excel to pdf. The basic descriptions of the leftfooter and leftheader properties returns or sets the alignment of text are different from those of the. Notes on variance, covariance, and summation operator by hiro kasahara properties of summation operator for a sequence of the values fx 1. This is a useful result since cones play such an important role in convex optimization. We also say that the set of nonnegative integers contains the set of positive integers.

The following section contains a brief overview of css3 properties. Today we introduce set theory, elements, and how to build sets. If we cut out sets a and b from the picture above, the remaining region in u, the universal set, is labeled, and is called the complement of the union of sets a and b. Basic concepts of set theory, functions and relations. They look like they could appear on a homework assignment in an undergraduate course. Hunter 1 department of mathematics, university of california at davis 1the author was supported in part by the nsf. Although we will not carry out the development of the real number system from these basic properties, it is useful to state them as a starting point for the study of real analysis and also to focus on one property, completeness, that is probablynew toyou. Two sets are equal if and only if they have the same elements. The main purpose of this is to allow us to develop techniques to prove more di. This material can be referred back to as needed in the subsequent chapters.

The spine of the set theoretic universe, and the most essential class of objects in the study of set theory, is the class of ordinals. Geometry learn with flashcards, games, and more for free. We can show that that by showing that note that 1 2 as 3 reason for 2. Sets and their properties university of british columbia. Properties of sets in this section we shall consider some of the basic properties of sets. The two basic properties to represent a set are explained below using various examples. One of the basic properties of an ordinal is that it is a wellordered set. Basic properties of probability there are several useful properties that can be derived from the axioms of. Here are three simple statements about sets and functions. This video is an updated version of the original video released over two years ago. Sets and set operations cs 441 discrete mathematics for cs m. The objects could be anything planets, squirrels, characters in shakespeares. An acquaintance with various examples and properties of wellordered sets is essential to the study of ordinals.

Georg cantor in the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains in predicate logic form sets as well. For example, a mathematician might be interested in knowing about sets s and t without caring at all whether the two sets are made of baseballs, books, letters, or numbers. Set theory basic set theory stanford encyclopedia of. Set intersections definition, properties, 3 examples. Closure is when all answers fall into the original set. Basic properties of convex sets there is also a version of theorem 3.

Review of basic concepts in probability padhraic smyth, department of computer science university of california, irvine january 2019 this set of notes is intended as a brief refresher on probability. This series of lessons cover the essential concepts of math set theory the basic ways of describing sets, use of set notation, finite sets, infinite sets, empty sets, subsets, universal sets, complement of a set, basic set operations including intersection and union of sets, using venn diagrams and simple applications of sets. Sets a set is a collection of objects, called the elements or members of the set. Sets are welldetermined collections that are completely characterized by their elements. The notion of set is taken as undefined, primitive, or basic, so we dont try to define what a set is, but we can give an informal description, describe. You should know the definition of each of the following properties of addition and how each can be used. Basic set theory a set is a many that allows itself to be thought of as a one. Locate all this information appropriately in a venn diagram. Examples of discrete structures built with the help of sets.

Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. Sets, relations and functions, sequences, sums, cardinality of sets richard mayr. Example 9 use the properties of sets to prove that for all the sets a and b a a. This chapter introduces set theory, mathematical in duction.

One is to list them explicitly, like you would find in a database of names. While we usually list the members of a set in a standard order if one is available there is no. Proving set identities algebraically alternatively, we can prove set. First, we shall consider some elementary properties of how certain sets related to each other. Set theory is the field of mathematics that deals with the properties of sets that are independent of the things that make up the set. In mathematics, a set is a welldefined collection of distinct objects, considered as an object in. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. For those of you new to abstract mathematics elementary does not mean simple though much of the material. Lecture notes 1 basic probability set theory elements of probability. Chapter 4 set theory \a set is a many that allows itself to be thought of as a one. The basic relation in set theory is that of elementhood, or membership. We will conclude the project by exploring a rather unusual world of in nite sets. Hauskrecht basic discrete structures discrete math study of the discrete structures used to represent discrete objects many discrete structures are built using sets sets collection of objects examples of discrete structures built with the help of sets.

In the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains in predicate logic form sets as well. Definition and properties for intersections of sets. So the set of outwear for kyesha would be listed as follows. Set theory half hollow hills central school district. Sets we discussed in class how to formally show that one set is a subset of another and how to show two sets are equal. Properties of set operation old dominion university. If a and b are sets, the union of a and b, written ab, is the set of all objects that belong to either a or b or both. Sets the width, style, and color for all four sides of an elements border. We also called these properties rules of arithmetic. These are the commutative, associative, and the distributve property.

Properties of sets two basic properties to represent a set solved. This page sets out the principles of sets, and the elements within them. Lecture notes 1 basic probability stanford university. We start with some basic properties of identities and inverses of groups given in the following proposition. For any two sets x and y, either there is a onetoone function from x into y or a onetoone function from y into x. Cantor set and its properties university of california. It sounds simple, but set theory is one of the basic building blocks for higher mathematics, so it helps to understand the basics well. However, we can extend them to include the properties of zero and one. The set t 2,3,1 is equal to s because they have the same members. Describing a set there are two distinct ways of describing the members of a set.