Many people collect various objects
and they classify them, e.g. "coins of the 10th century", "French paintings",
etc.
Since ancient history people classified
the numbers in categories, e.g. "the prime numbers", "the even numbers",
etc.
Categories, like the above or even groups
of objects of the same kind or not, which can be distinguished, are called
sets.
According to the mathematician Cantor:
"Sets are every collection of objects which derive from our experience or are our intellectual creations, that can be distinguished the one from the other and are well defined." 
To represent a set we use one of the letters of the Latin alphabet. If we want to denote that x is a member of the set A, we write and we read " x is a member of A". On the other hand, if we want to denote that the x is not a member of A we write and we read " x is not a member of A".
A set can be represented with the ways described bellow:
We say that two sets A and B are equal
when they have exactly the same elements and we write A=B
For example if A={ 0 , 1 , 2 } and B={
2 , 1 , 0} then A=B.
We say that a set A is a subset of B when
every member of A is a member of B and we write .
For example if A={ 0 , 1} and B={1 , 0
, 2 } then .
Immediate consequences of these definitions
are:
