Another particular example about sets, comes from the field of history. The whole set of Presidents of the United States offers a very good example.

Let consider the Presidents of the United States of this century. Mathematically, we can express this relation in the following way:

{Roosevelt, Taft, Wilson, Harding, Coolidge,..., Reagan, Bush, Clinton}.

Until now, we have seen examples about sets in diverse fields outside mathematics. At this point, it is necessary talk a little about the symbolism used in algebra of sets.

As we stated earlier, sets are collection of objects or things that they have certain characteristics in common. In order to denote a set, it is usually use capital letters to identify sets. For example:

W is the set of days of the week.

W = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

Please note the use of the symbol "{ }" and commas separating the elements of the set. It means, that the elements of the set W are the days of the week, that is, Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. In other words, these days belong to set W.

What about another sets in mathematics per se? You can try forming the following sets given the following statements:

The set of seasons of the year.

The set of prime numbers.

The set of numbers divided by two.

The set of numbers divided by two and three.

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