sets

sets is a collection of objects & a set is denoted by listing elements between braces

for example { 1 , 4  ,  8 }
and we do not count multiplicities we regard the set { 1 , 2 , 2 , 2 , 3 , 3 } as identical to the set { 1 , 2 , 3 } and order is not significant in sets and the set { 1 , 2 , 3 } is equivalent to the set { 3 , 2 , 1 }
and in enumerating the elements of the sets we use ellipse to indicate patterns . we denote the positive integers as { 1 , 2 , 3 , ......... } . we also denote the sets with the notation { x : condition on x } for sets that are more easily described than enumerated and this is read as " the set of elements  x such that x ....." .
and the Cartesian product of two sets is the set of the ordered pairs

and the Cartesian product of n sets is  the set of ordered n-tuples