Thinking Mathematically Basic Set Concepts

A “set” is a collection of objects. Each object is called an “element” of the set. Often the objects in a set are listed and are enclosed in “braces.” For example the set of integers between 1 and 5 can be written {2, 3, 4}.

Representing Sets Word Description: Describe the set in your own words, but be specific so the elements are clearly defined. Roster Method: List each element, separated by commas, in braces. Set-Builder Notation: {x | x is … word description}.

The Empty Set The empty set, also called the null set, is the set that contains no elements. The empty set is represented by { } or Ø

Basic Set Concepts Note that the number zero does not represent the empty set. If you have a bank account with no money in the account, your balance is represented by the number zero. But if you do not have an account in the bank, your situation can be represented by the empty set.

The Notation  and  The symbol  is used to indicate that an object is an element of a set. The symbol  is used to replace the words “is an element of” The symbol  is used to indicate that an object is not an element of a set. The symbol  is used to replace the words “is not an element of”

The Set of Natural Numbers N = {1,2,3,4,5,…}

Definition of a Set’s Cardinal Number The cardinal number of set A, represented by n(A), is the number of elements in set A. The symbol n(A) is read “n of A”.

Definition of a Finite Set Set A is a finite set if n(A) = 0 or n(A) is a natural number. A set that is not finite is called an infinite set.

Definition of Equality of Sets Set A is equal to set B means that set A and set B contain exactly the same elements, regardless of order or possible repetition of elements. We symbolize the equality of sets A and B using the statement A = B.

Definition of Equivalent Sets Set A is equivalent to set B means that set A and set B contain the same number of elements. For equivalent sets, n(A) = n(B).

Thinking Mathematically Basic Set Concepts