All the elements of a set are distinct.
In other words: no element may `occur'
more than once in a set.
This is because an object x
cannot be member of a set in more than one way.
Either x is a member of S or not.
2.
The elements of a set are not ordered in any way.
To know,
that x and
y
are members of a set cannot tell us in which order
they occur.
3.
A set must be distinguished from its description.
For instance, the following expressions are clearly different:
{ 2, 3, 4 }, { 3, 2, 4 }, { 2, 2, 3, 4, 4, 4 }
{ n | 2 n 4 }, { m | 2 m 4 }, { n | 1 < n < 5 }
However, all these descriptions are equivalent:
They denote the same set.