A set is a collection of elements. Sets and elements have
names:
Naturals = {1,2,3,...}
A = {1,2,3, ... , 10}
Students = {JohnDoe, JaneBrown, ...
}
USCities = {Albuquerque, Berkeley, Oakland,
...}
Books = {(Lee, Digital Communications), (Walrand,
Communication Networks), ...}
An element is or is not a member of a set:
4 Î
A, 11 ÏA
A set can be defined as an unordered list of
elements (enclosed in braces, { }), without duplication. So
if B = {10,9, ... , 1}, then A = B
Sometimes, order matters, in which case we define an ordered set,
which is a set plus an ordering relation
"<"
between members of the set. For example, Time might be represented
by the ordered set Reals plus an ordering relation R
Ì Reals
´ Reals where (x, y)
Î R if x <
y. This represents the usual ordering relation on real numbers (i.e. the
ordering relation that allows us to say that 2.0
<
3.1). The members of the ordered set Time are the same as the
members of the set Reals.