EECS20N: Signals and Systems


  • An expression like n 5 is a predicate (in the variable n) or predicate over the set Naturals. A predicate becomes an assertion whenever a value is assigned to its variable. A value satisfies a predicate if the predicate is true at that value:
n 5 is satisfied at n = 5 but it is not satisfied at n = 7.
  • Use predicate Pred(x) to define new set NewSet from existing set Set
NewSet = {x Set | Pred (x) } (*)
  • Examples
{1,2,3,4,5} = { nNaturals | n 5 }

TallStudents = { nameStudents | name is more than 6 feet tall}

  • A predicate over a set can involve an expression in any attribute of its elements.
  • The variable name x in (*) is not significant--replacing x by y makes no difference:
{xSet | Pred(x) } = {ySet| Pred(y) } That is why x in (*) is called a dummy variable.