L04 - Sets 1 Sets Informally: A set is a collection of...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Sets 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sets Informally: A set is a collection of (mathematical) objects, with the collection treated as a single mathematical object. real numbers, complex numbers, C integers, All students in our class Examples:
Background image of page 2
Defining Sets Sets can be defined directly: e.g. {1,2,4,8,16,32,…}, {CSC1130,CSC2110,…} Order, number of occurence are not important. e.g. {A,B,C} = {C,B,A} = {A,A,B,C,B} A set can be an element of another set. {1,{2},{3,{4}}}
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Defining Sets by Predicates The set of prime numbers : ) {} ( | x AP x The set of elements , x, in A such that P(x) is true.
Background image of page 4
Commonly Used Sets N = {0, 1, 2, 3, …}, the set of natural numbers Z = {…, -2, -1, 0, 1, 2, …}, the set of integers Z + = {1, 2, 3, …}, the set of positive integers Q = {p/q | p Z, q Z, and q 0}, the set of rational numbers R , the set of real numbers
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Special Sets Empty Set (null set) : a set that has no elements, denoted by ф or {}. Example: The set of all positive integers that are greater than their squares is an empty set. Singleton set : a set with one element Compare: and { } Ф : an empty set. Think of this as an empty folder { }: a set with one element. The element is an empty set. Think of this as an folder with an empty folder in it.
Background image of page 6
Venn Diagrams Represent sets graphically The universal set U, which contains all the objects under consideration, is represented by a rectangle. The set varies depending on which objects are of interest. Inside the rectangle, circles or other geometrical figures are used to represent sets. Sometimes points are used to represent the particular elements of the set. 7 a V e i o u U
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
{7, “Albert”, /2, T } Membership xA x is an element of A x is in A /2 {7, “Albert”, /2, T } /3 {7, “Albert”, /2, T } 14/2 {7, “Albert”, /2, T } 7  2/3  Examples:
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 31

L04 - Sets 1 Sets Informally: A set is a collection of...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online