EECS20N: Signals and Systems

Sets

  • 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 ∈ A, 11 ∉A
  • 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 ⊂ 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.