Sets and numbers pdf

Prime numbers, existence and uniqueness of prime factorisation and nonuniqueness in other number systems, e. Our milemate sets include a growing range of timken 454series wheel bearings designed specifically for severeduty, dual and wide singletire applications. Here are printable sets all free downloads that will help you set up your calendar dates for the whole year including fall, spring and holidays i hope you can choose from your favorites or spice up your current calendar to make it your own. Sets, numbers, and systems book 2 singer mathematics program. In mathematics also, we come across collections, for example, of natural numbers, points, prime numbers, etc. This then laid down the foundations for a fundamental way of thinking. We can represent this relationship through venn diagram in the following way. This video is an updated version of the original video released over two years ago. In fact it would be better to stay away from using languages like english to describe sets. A is the set whose members are the first four positive whole numbers. Boole developed an algebra of sets where the elements of the sets could be not just numbers but anything. The union of any two given sets a and b is the set c which consists of all those elements which are either in a. The set of real numbers can be drawn as a line called the number line.

Borel and lebesgue, mathematicians didnt recognize measurable sets of real numbers. In this lesson, we will look at some of the most common number sets and a few of their characteristics. For example, the set of days of the week is a set that contains 7 objects. Lets describe the certain sets that exist as well as their properties. Play with teen numbers up to 20, ordinal numbers, fractions, andor decimal numbers. W p2p0 s1s2 g 5keu6t 2ag esbopfltew vaermep ul tl vcc. Use the numbers for various craft projects, number and math learning activities, games, and other classroom activities. For example, the set of natural numbers is a subset of set of whole numbers which is a subset of integers. A set is a collection of objects, called elements of the set. Refer to the diagram to answer the questions below. Two sets are equal if and only if they have the same elements. Here are printable sets all free downloads that will help you set up your calendar dates for the whole year including fall, spring and holidays. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions.

Use 10frame cards attached instead of regular playing cards. If there is a onetoone function from x into y and also a onetoone function from y into x, then there is a onetoone function from x onto y. A set which contains limited number of elements is called a finite set. You will need three sets of 1 to 10 for each partnership. About sets of real numbers worksheet sets of real numbers worksheet. Here a is a set of five positive odd numbers less than 10. An introduction to proofs, logic, sets, and numbers introduces key concepts from logic and set theory as well as the fundamental definitions of algebra to prepare readers for further study in the. Is s is one of those sets then we also use the following notations.

T is the collection of all objects that are in both sets. Today we introduce set theory, elements, and how to build sets. The structure n, 0, s is a model of the peano axioms. Sets, functions, relations northwestern university. Precisely matched sets allow bearings to more evenly distribute loads, extending bearing life. The set n of natural numbers is defined in this system as the smallest set containing 0 and closed under the successor function s defined by sn n. Certain sets of numbers, such as the real numbers r, are referred to regularly enough to merit their own special symbol.

Hardegree, infinite sets and infinite sizes page 3 of 16 most mathematicians and philosophers, however, are perfectly happy to grant sethood to the natural numbers, and even more vast collections, and accordingly must come to terms with the question. The in nite sets we use are derived from the natural and real numbers, about which we have a direct intuitive understanding. I argue that benacerrafs argument is not as strong as. So sets can consist of elements of various natures. 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. The set of rational numbers is defined by here is the set of rational numbers, all those numbers that can be expressed as a ratio of two integers. The objects which form a set are called its members or elements. Since the number of elements is limited, a is a finite set. For now, we can express the relationship between all types of. In this paper i discuss the intuition behind freges and russells definitions of numbers as sets, as well as benacerrafs criticism of it. Addressing the importance of constructing and understanding mathematical proofs, fundamentals of mathematics. The order of the elements in a set doesnt contribute anything new. Sets, numbers, and systems book 2 singer mathematics.

The following exercises will help you further understand the properties that hold true for each of the sets of numbers and the relationships among them. Basic concepts of set theory, functions and relations. The integers, rational numbers, and algebraic numbers are countably. W 2 lit and ir are two of very many real numbers that are not rational numbers. Settheoretic definition of natural numbers wikipedia. A grade 5 class is a finite set, as the number of students is a fixed number. Denumerable sets are infinite, but are equivalent to the natural numbers 1, 2, 3. Video for interval notationset builder notationroster notation. In the world of mathematics we have categorized all the numbers that exist into certain sets. For now, we can express the relationship between all types of infinite and countable sets with the following venn diagram. Sets are an important aspect of math which kids can apply in their everyday life. The objects that make up a set also known as the set s elements or members can be anything. Furthermore, the set of rational numbers includes all those numbers whose decimal representation terminates or repeats. Theyre quite useful for various arts and craft projects, number and math learning activities, games.

Georg cantor, one of the founders of set theory, gave the following definition of a set at the beginning of his beitrage zur. An accessible introduction to abstract mathematics with an emphasis on proof writing. X 2, 3, 5, 7, 11, 17 cs 441 discrete mathematics for cs m. Jr is the set of numbers that can be used to measure a distance, or the negative of a number used to measure a distance. For example, the set of days of the week is asetthatcontains7objects. Similar issues arise with the notion of arbitrary subsets, functions, and relations. Now, at first glance they may not seem equal, so we may have to examine them closely. Play with numbers 1 to 5, slowly adding numbers to the game as the first five are mastered. Other standard sets include the integers z, the positive integers n also called the natural numbers, the rational numbers q the set of all fractions, and the complex numbers c. A set is a collection of objects usually of the mathematical kind, such as numbers or points in space etc. The set of complex numbers includes all the other sets of numbers. This topic also integrates and aspect of classification of numbers or objects. The existence of the set n is equivalent to the axiom of infinity in zf set theory. Organize a classroom by getting your calendar numbers ready to go for the whole year.

We then discuss, in this order, operations on classes and sets, relations on classes and sets, functions, construction of numbers beginning with the natural numbers followed by the rational numbers and real numbers, in. Relating number sets we will continue our focus on the number line and the relationships among the various types of numbers that make up the real number system. Nov 28, 20 sets are an important aspect of math which kids can apply in their everyday life. Bertrand russell, a great mathematician and philosopher of the 20th century, said that the greatest discovery of the 19th century was the. Sep 24, 2017 organize a classroom by getting your calendar numbers ready to go for the whole year. The number m is called an upper bound for the set s.

Combinations of real and imaginary numbers make up the complex numbers. Definition set a set is a welldefined collection of objects. First a quick mention about how sets are described. Not every collection of numbers with a description is a set. In symbolic notation the size of a set s is written s.

Numbers among the most common sets appearing in math are sets of numbers. But they were there, just as the planet pluto existed before it was discovered around 1930. Cardinal and ordinal numbers math 6300 klaus kaiser april 9, 2007. Each of the above sets of numbers has an infinite number of elements, and each can be considered to be a proper subset of the sets listed below it. Together all these sets combined make up the set of real numbers. Two sets are equal if they have precisely the same members. Corresponding bold face letters are also a common notation for these sets of numbers. Its ubiquitousness comes from the fact that integers and their properties are wellknown to mathematicians and nonmathematicians. Natural numbers, integers, rationals and real numbers.

Classify each of the numbers given below by naming the set or sets to which it belongs. Some authors do not include 0 in the set of natural numbers. Worksheet on sets of real numbers is much useful to the students who would like to practice problems on classifying rational numbers. A set a is a subset of a set b iff every element of a is also an element of b. We are going to claim that there are sets, in particular an empty set and an in. Duplicates dont contribute anythi ng new to a set, so remove them.

Sets, numbers, and systems book 2 singer mathematics program patrick suppes, bruce meserve, phyllis sears on. S is called bounded above if there is a number m so that any x. A set can be represented by listing its elements between braces. Sets and elements set theory is a basis of modern mathematics, and notions of set theory are used in all. Here are some algebraic equations, and the number set needed to solve them. Given a set s, the power set of s is the set of all subsets of s. This quiz was designed for the wicomico county alc. Sets in general will be denoted here by capital letters.

By inspection we see that 0 is a member of the integers, the rational numbers since \\large \frac01 0\, and the real numbers. We aim to prove that the irrational numbers and the real numbers are both uncountable sets. If x is a subset of the real numbers, then either there is a onetoone. 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 important properties of sets, and give. I hope you can choose from your favorites or spice up your current calendar to make it your own. A set is a welldefined collection of distinct objects. The evolution of our number system can be summarized roughly as the series of set inclusions.