This document discusses sets and their properties. It defines what a set is and the different ways to describe a set using word descriptions, listings, or set-builder notation. It discusses elements and members of sets, and whether certain values are elements of example sets. It also defines key set concepts like cardinality (the number of elements in a set), finite vs infinite sets, and why cardinal numbers cannot be determined for infinite sets.

1. Set Theory Sets, elements, kinds of numbers

2. Sets Set- A collection (usually of numbers) People tend to want to group things. A set is amthematical way to group things, usually numbers Elements / Members The things (numbers) that make up a set

3. Sets 3 ways to describe a set Word description All the odd numbers between 11 and 35 Listing Method { 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33} Notice the { } symbols. The denote a SET Commas are essential Set-Builder Notation {x|x is an odd number between 11 and 35 } X such that x is an odd number…

4. Sets Set-builder notation Uses a variable, usually x The variable before the line represents elements of a set, in general After line- state criteria for the set Sets are given names for instance if we use E E= {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 35, 27, 29, 31, 33, 35, 37, 39, 41}

5. Sets Set notation can be shortened by establishing a pattern, using ellipses E= {1, 3, 5, 7, ……….. 39, 41} A set with nothing (no elements) Empty set or null set Notated by ø or {} Not {ø} this is a set with one element; ø

6. Elements of Sets q ϵ E q is an element of e Are the following statements true? 3 ϵ {1, 2, 5, 9, 13} 0 ϵ {0, 1, 2, 3} 0.5 ϵ {0.2, 0.5, 0.8} No Yes Yes

7. Elements of Sets The number of elements in a set is called the Cardinal Number or Cardinality of the set n(A) Read as n of A Means number of elements in set A Find n(D) D= {3, 7, 26, 678, 920} N(D)= 5

8. Elements of Sets If the same element is listed more than once in a set, you don’t count them more than once when finding the cardinality of a set Find n (R) R= {0,1, 1, 2, 2, 3, 3} N(R) = 4

9. Elements of Sets Sets can either be infinite or finite There can be an amount that could eventually be counted. These are Finite Sets We can find the Cardinal number for these sets Numbers go on forever without ending. Therefore, some sets can go on forever. These are Infinite Sets It is not possible to find a cardinal number for infinite sets Why can’t we find a cardinal number for infinite sets?