This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 6.2: Sets and Counting A set is a welldefined collection of objects, called elements . We can express sets by listing their elements, or by a definition. Example: A set expressed by listing: A = { 1 , 2 , 3 } A set expressed by a definition: B = { x  x is even } Just like matrices, we can name sets with capital letters. Sets may have a finite number of elements, like A , or an infinite number of elements, like B . We will focus on sets with a finite number of elements. We use the symbol to mean is an element of, and the symbol / to mean is not an element of. For example, we could write 3 A , because 3 is one of the elements of A . We could also write 4 / A because 4 is not one of the elements of A . We use the symbol to show that one set is completely contained in another. When we write something like A B , we read it as A is a subset of B , and it means that everything inside of A is also inside of B . We use the symbol notsubseteql when we wish to say that one set is not com pletely contained in another. Example: Let A = { 1 , 5 , 7 } , B = { 1 , 3 , 5 , 7 , 10 } , and C = { 1 , 2 , 5 } . Since everything inside of A is also inside of B , we can write that A B . Since not everything inside of C is also inside of B , we can write C notsubseteql B . We usually talk about sets in relation to a larger set, the universal set , or universe . The universe is a set which contains all the sets under discussion. We use the symbol U for the universe. When a set has no elements, we call it the empty set . We use the symbol for the empty set. 1 We can visualize sets by the use of a Venn diagram . With a Venn diagram, we represent the universal set as a large rectangle, and the other sets as circles within the universe....
View
Full
Document
This note was uploaded on 02/05/2011 for the course MATH 377 taught by Professor Stephenlang during the Spring '11 term at University of Victoria.
 Spring '11
 stephenlang
 Calculus, Sets, Counting

Click to edit the document details