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 Set:  A collection of numbers, geometric figures, letters, or other objects that have some characteristic in common.

The members of the set are often called the elements of the set. A set is usually named using capital letters. Sets can be defined in at least 3 ways:

1) Listing the members enclosed in brackets, either "{ }" or "( )", with members of the set separated by commas.

2) Using a verbal description.

3) Using set-builder notation.

An example of a set is the set of integers. That was a verbal description for the set. We can also define the set of integers using the other two ways to define sets:

Listing: I = {, -3, -2, -1, 0, 1, 2, 3, ...}

Set-Builder Notation: I = {x | x is an integer}. This is read: "I is the set of all x such that x is an integer."

We say two sets are equal when they have the same elements. For example, if A is the set of primary colors and B = {red, yellow, blue}, then A and B are equal. We could write A = B. Another example might be if W = {0, 1, 2, 3, ...} and T is the set of whole numbers, then we can say W = T. If the sets do not have the same elements, they are not equal. For example, if W = {0, 1, 2, 3, ...} and N = {1, 2, 3, ...}, then W is not equal to N since W has an element that N does not have: the number 0. We can write W  N.

When we list sets, we use two rules:

1) The same element is not listed more than once. So the set A =  {1, 2, 3, 3, 4, 5} should be written as A = {1, 2, 3, 4, 5}

2) The order of the elements does not matter. So the set A = {1, 2, 3, 4, 5} = {1, 3, 5, 2, 4}.

We use the symbol to indicate that an object is a member of a particular set. The symbol is used to indicate that an object is not a member of a particular set. For example, if I represents the set of all integers, then -100  I but 1/2  I.

The set with no elements is called the empty or null set. Both of the symbols {} and are commonly used to denote this set. For example, the set of all integers that are both negative and positive at the same time is the empty set.