We have three ways of describing sets:
        1.   by name or verbal description of the elements of a set,
        2.   by roster (list) form by listing the elements separated by commas and using braces to enclose the list, or
        3.   by set-builder notation that uses a variable and a rule to describe the elements of a set.

Example:
        Let S represent the collection of states that border Minnesota (verbal)
        S = {North Dakota, South Dakota, Iowa, Wisconsin, Michigan} (roster)
        S = {x : x is a state bordering Minnesota} (set-builder)

        The set-builder form is read as “S is the set of all x such that x is a state bordering Minnesota.”

Example: 
        Let N represent the collection of counting numbers (verbal)
        N = {1, 2, 3, 4, …} (roster)
        N = {x : x is a counting number} (set-builder)

Example: 
        The set of presidents of the U.S. who were still alive June 15, 2009 (verbal)
        {Jimmy Carter, George H. W. Bush, Bill Clinton, George W. Bush, Barack Obama} (roster)
        {x : x was a President of the U.S. who was still alive June 15, 2009} (set-builder)

        The set-builder form is read, “the set of all objects such that the object was a president of the U.S. who was still alive June 15, 2009.”

Example: 
        The counting number multiples of 5 that are less than 30 (verbal)
       {5, 10, 15, 20, 25} (roster)
       {x : x is a counting number multiple of 5 that is less than 30} (set-builder)