Math

• Georg Cantor


  German Mathematician who started Set Theory as a separate mathematical discipline
• Set Theory


  A mathematical theory that deals with the properties of well defined collection of objects
• Sets

  A collection of objects or things
• Sets


  • The set of students attending college in the Philippines
  • The set of natural numbers: 1, 2, 3, etc.
• Elements (or members)


  The objects or things that make up a set
• Braces {}


  Sets are usually represented by listing elements, separated by COMMAS within BRACES
• Sets


  • {5, 7, 9}
  • {A, D, F, H, K}
• A Set may contain just a few elements few elements or no elements
• Set name

  Usually named by a Capital Letter such as A, N, W, etc.
• Elements of sets

  Usually written in lowercase
• Expression A = {m, t, c}

  Read as "A is the set whose elements are m, t, and c"
• Sets

  • The set of planets in our solar system
  • The set of natural numbers greater than 5
• Cardinality of a set

  A measure of a set's size, meaning the number of elements in the set
• Cardinality


  • A = {1, 2, 4} has cardinality of 3
• Symbol ∈


  The expression x ∈ A is read as "x is an element of set A"
• Roster Method


  Representing a set by listing its members
• When the number of elements in a set is large, the roster notation is modified to indicate the pattern
• Rule Method (Set-Builder Notation)


  Representing a set by giving a rule describing its members
• Equal Sets

  Two sets are equal if they have exactly the same elements
• Equivalent Sets

  Two sets have the same number of elements
• Empty Set


  A set having no elements, represented as {} or ∅
• Empty Set


  • The set of all people in your math class who are 10 ft. tall
• Singleton Set


  A set containing only one element
• Singleton Sets


  • The set of months having less than 30 Days: {February}

  The set of all even prime numbers: {2}
• Finite Set


  A set that contains a limited number of elements
• Finite Sets


  • Colors of a Rainbow: {Red, Orange, Yellow, Green, Blue, Indigo, Violet}

  Y = {1, 2, 3, ..., 10}
• Infinite Set


  A set that contains an unlimited number of elements
• Infinite Sets


  • Integers: {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}

  P = {All the people in the world}
• Universal Set


  The set containing all elements and of which all other sets are subsets
• Subset


  Set A is a subset of set B if every element in A is also an element in B
• Proper Subset


  Set A is a proper subset of set B if there's at least one element in B not contained in A
• Superset


  B is a superset of A if every element in A is also in B
• Proper Superset


  B is a proper superset of A if A contains at least one element that is not in B
• Power Set


  The set of all the subsets of a set
• Joint Set


  Sets that have elements in common
• Joint Sets


  • A={1, 2} and B={2, 3} are joint because they share the element 2
• Disjoint Set

  Sets that do not have elements in common
• Disjoint Sets

  • A={1, 2} and B={3, 4} are disjoint because they do not have elements in common
• Venn Diagrams


  Diagrams used to represent sets, relations between sets, and operations on sets
• Union


  The set of all elements that are in either set A or set B, or both