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. Sets a set is a collection of objects, called the elements or members of the set. Note the close similarity between these properties and their corresponding properties for. One of the basic properties of an ordinal is that it is a wellordered set. 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. 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. Here are three simple statements about sets and functions. Geometry learn with flashcards, games, and more for free. The basic syntax of the exportasfixedformat method is generally as follows. So the set of outwear for kyesha would be listed as follows. Basic concepts of set theory, functions and relations. Sets and their properties university of british columbia.
Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. We can show that that by showing that note that 1 2 as 3 reason for 2. Properties of sets two basic properties to represent a set solved. This page sets out the principles of sets, and the elements within them. 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. In other words, we wont describe what a set is, we will describe what can be done with sets. They look like they could appear on a homework assignment in an undergraduate course.
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. 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. In the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains in predicate logic form sets as well. An acquaintance with various examples and properties of wellordered sets is essential to the study of ordinals. 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. Basic building block for types of objects in discrete mathematics. Properties of set operation old dominion university. This material can be referred back to as needed in the subsequent chapters. Today we introduce set theory, elements, and how to build sets. Example 9 use the properties of sets to prove that for all the sets a and b a a. The properties of these sets of numbers that make them distinct are. First, we shall consider some elementary properties of how certain sets related to each other.
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. The most basic properties are that a set can have elements, and that two sets are equal. Intuitivelly, a set is a collection of objects of any kind, which we call the elements of a set. The set t 2,3,1 is equal to s because they have the same members. With each number, place it in the appropriate region. Cantor set and its properties university of california.
Duplicates dont contribute anythi ng new to a set, so remove them. Chapter 4 set theory nanyang technological university. Georg cantor this chapter introduces set theory, mathematical induction, and formalizes the notion of mathematical functions. 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. One is to list them explicitly, like you would find in a database of names. We also called these properties rules of arithmetic. 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. The order of the elements in a set doesnt contribute anything new. 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. Proving set identities algebraically alternatively, we can prove set. Sets are welldetermined collections that are completely characterized by their elements. Basic properties of convex sets there is also a version of theorem 3. Two sets are equal if and only if they have the same elements. The basic descriptions of the leftfooter and leftheader properties returns or sets the alignment of text are different from those of the.
You may need to consult a reference, such as the internet or an encyclopedia. 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. 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. Sets and set operations cs 441 discrete mathematics for cs m. We start with some basic properties of identities and inverses of groups given in the following proposition. There are two methods of representing a set i roaster or tabular form ii set builder form 1. Sets, relations and functions, sequences, sums, cardinality of sets richard mayr. The main purpose of this is to allow us to develop techniques to prove more di. A set is a collection of objects that have something in common or follow a rule. However, we can extend them to include the properties of zero and one. Set theory half hollow hills central school district. The two basic properties to represent a set are explained below using various examples. Notes on variance, covariance, and summation operator by hiro kasahara properties of summation operator for a sequence of the values fx 1.
Basic properties of set operations are discussed here. Set theory basic set theory stanford encyclopedia of. The following section contains a brief overview of css3 properties. Basic set theory a set is a many that allows itself to be thought of as a one. This chapter introduces set theory, mathematical in duction. 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. Properties of sets in this section we shall consider some of the basic properties of sets.
The objects could be anything planets, squirrels, characters in shakespeares. Sets the width, style, and color for all four sides of an elements border. Set notation uses curly braces, with elements separated by commas. Definition and properties for intersections of sets. 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. Lecture notes 1 basic probability set theory elements of probability. This video is an updated version of the original video released over two years ago. 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. One of the goals of group theory is to classify all group structures on all sets in a useful way. Lecture notes 1 basic probability stanford university. Stepbystep guide and 10 code examples to export excel to pdf. Set theory examples, body, basic, part, properties of sets. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.
It sounds simple, but set theory is one of the basic building blocks for higher mathematics, so it helps to understand the basics well. For those of you new to abstract mathematics elementary does not mean simple though much of the material. Set intersections definition, properties, 3 examples. Adding sets and quanti ers to this yields firstorder logic, which is the. Describing a set there are two distinct ways of describing the members of a set. Chapter 4 set theory \a set is a many that allows itself to be thought of as a one. Closure is when all answers fall into the original set. Properties of set operation subjects to be learned. We also say that the set of nonnegative integers contains the set of positive integers. Set operations and venn diagrams university of hawaii.
We will conclude the project by exploring a rather unusual world of in nite sets. Locate all this information appropriately in a venn diagram. Will work on this in the class, but you can find an answer at the back of the textbook. The basic relation in set theory is that of elementhood, or membership. These are the commutative, associative, and the distributve property. 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. Examples of discrete structures built with the help of sets. This is a useful result since cones play such an important role in convex optimization. When two numbers are added, the sum is the same regardless of the order in which the numbers are added. Thus, two sets are equal if and only if they have exactly the same elements.