81 Views

Download Presentation
##### 2.1 Sets and Whole Numbers

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**2.1 Sets and Whole Numbers**Remember to Silence Your Cell Phone and Put It In Your Bag!**Sets**• Intuitive definition of Set – A collection of objects • List the objects of a set within braces { } • When listing the objects of a set, separate them with commas • Use a capital letter to name a set • Order of the elements is not important • Element x A, x A • A versus a**One-to-One Correspondence**Sets A and B have one-to-one correspondence iff each element of A can be paired with exactly one element of B and each element of B can be paired with exactly one element of A.**Equal and Equivalent Sets**• Sets A and B are equal sets, symbolized by A = B, iff each element of A is also an element of B and each element of B is also an element of A. • Sets A and B are equivalent sets, symbolized by A B, iff there is a one-to-one correspondence between A and B.**Subset and Proper Subset**• For all sets A and B, A is a subset of B, symbolized as A B, iff each element of A is also an element of B. • For all sets A and B, A is a proper subset of B, symbolized by A B, iff A is a subset of B and there is at least one element of B that is not an element of A.**Additional Terminology**• The Universal Set U • Empty Set or Null Set { } • Finite Set • Infinite Set**The Complement of a Set**• The complement of set A, written Ᾱ, consists of all of the elements in U that are not in A.**Whole Number**• A whole number is the unique characteristic embodied in each finite set and all the sets equivalent to it. • The number of elements in set A is expressed as n(A) and is called the cardinality of set A.**Counting**Counting is the process that enables people systematically to associate a whole number with a set of objects.**Ordering Whole Numbers**• For whole numbers a and b and sets A and B, where n(A) = a and n(B) = b, a is less than b, symbolized as a < b, iff A is equivalent to a proper subset of B. • a is greater than b, written a > b, iff b < a**Special Subsets of the Set of Whole Numbers**• Counting Numbers or Natural Numbers {1, 2, 3, 4, . . . } • Whole Numbers {0, 1, 2, 3, . . . } • Even Whole Numbers {0, 2, 4, 6, . . . } • Odd Whole Numbers {1, 3, 5, 7, . . . }**Three Types of Numbers**• Nominal Number • Ordinal Number • Cardinal Number**An announcer says:**"The student with ID number 50768-973 has just won second prize--four tickets to the big game this Saturday."