Sets
- A set is a collection of elements. Sets and elements have names:
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:
- A set can be defined as an unordered list of elements (enclosed in braces, { }), without duplication. So
- 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 ⊂ Reals ´ Reals where (x, y) ∈ 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.