Discrete Math Notes:
Chapter 1: Logic and Sets, Sections 1.11
Terms:
Set, a collection of objects
Elements, the objects in a set
roster notation, a set is a list of the elements enclosed in curly braces with the individual elements separated by commas
empty set, the set with no elements, also denoted by the symbol
null set, another name for an empty set
finite set, a set that is either empty or whose elements can be numbered 1 through n for some positive integer n.
infinite set, a set that is not finite
cardinality, a finite set A, denoted by IAI, is the number of elements in A. If A = { 2, 4, 6, 10 }, then |A| = 4.
x > 0, A number x is said to be positive
x < 0, A number x is negative
x 0, A number x is non-negative
R*, The superscript + is used to indicate the positive elements of a particular set; the set of all positive real numbers
set builder notation, a set is defined by specifying that the set includes all elements in a larger set that also satisfy certain conditions
universal set, usually denoted by the variable U, is a set that contains all elements mentioned in a particular context
Venn diagrams, Sets often represented pictorially are called this
Subset, if every element in A is also an element of B,then A is considered a subset
proper subset, If A B and there is an element of B that is not an element of A (i.e.,A B)
Overview:
A finite set is one whose elements may be numbered 1 through n for some positive integer n
and is either empty or has no elements. A non-finite set is called an infinite set. The number of items in a finite set A, indicated byAl, is its cardinality. If A = {2, 4, 6, 10}, then |A= 4.The empty set|Ol has a cardinality of zero. The empty set is indicated by the symbol O and is a set with no elements. The empty set is also known as the null set and is represented by the brackets. Because the empty set contains no items, an is true for any element a, a # O. A group of objects is referred to as a set. Objects can be of different types, including book titles, bridge names, and rational numbers. The focus of this material is on sets of mathematical objects, such as numbers. Elements are the objects that make up a set. A collection of elements can include elements of many types, such as the number 2, a strawberry, and a monkey. The elements that make up a set are specified by declaring which ones belong to it. If a set has a small number of elements, listing the elements is the simplest approach to express it. A set is defined in roster notation as a list of elements enclosed in curly braces with commas separating the distinct eleme