In order to better organize things, we often put them into sets.  Simply stated, a set is a collection of objects. 

A set must be well-defined, meaning that its contents can be clearly determined.

For example, consider the set of a collection of great mathematicians.

Whether or not a person belongs to this collection depends on how we interpret the word great.  Therefore, this set is not well-defined.

Sets can be indicated several different ways, and three of the most common ways are using word description, roster form, or set-builder notation. 

One method to indicate a set is not necessarily better than another. 

When in doubt, it is usually best to describe larger sets with set-builder notation or a word description.

Set-builder notation:

Example:

1. Write the set including the numbers 3, 5, 7, 9, 11, 13, 15, 17, and 19 in set-builder notation.

{x | x ∈ N and 3 ≤ x ≤ 19 }

2. Write the set including the natural numbers 56, 57, 58, 59, and so on in set-builder notation.  

{x | x ∈ N and x ≥ 56}