Set Concepts

• A set os a collection of objects.
• The objects are called members or elements.
• Some examples:
  • Let D be the set of the days of the week.
  • Let N be the set of the numbers the counting numbers bigger than one.
• A set is well defined if the elements can be clearly identified
  • The two sets above are well defined.
  • The set of the best math 104 teachers at Edinboro is not.
• Sets can be written in descriptive format
  • let L be the set of the letters in the alphabet.
  • let, an upper case letter , be the set of, a description of the set
• or in roster format
  • Let D = { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
  • Let N = { 1, 2, 3, ...}
  • Let L = { a, b, ... z, A, B, ... Z}
• Set builder notation is for mathematical sets (mostly)
  • Let T be the integers between 3 and 33.
  • T = { 3, 4, 5, ... 33}
  • T = { t | t ∈ N, 3 ≤ t ≤ 33}
• The symbol ∈ means that the element on the right is an element of the set on the left.
  • The symbol ∉
  • Monday ∈ D
  • {Tuesday} ∉ D
• n(D) is the number of elements in the set D, n(D) = 7
• n(T) = 31
• if n(S) ∈ N, or n(S) = 0 then the set S is finite, otherwise it is infinate.
• n(N) ∉ N, so N is an infinate set.
• Two sets, A and B, are equivelent if n(A) = n(B)
• Two sets are equal if n(A) = n(B) and every element of A is also an element of B.
• The empty set ∅ or {} contains no elements.
• The universal set (U) is the set of all elements under consideration.