SETS

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• SETS

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What is a set?

• A set is a collection of objects.
• You can have a set of books
• a set of china
• a set of pool balls

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Elements of a set

• The individual members of the set are called the
  elements of the set.
• In set notation,
• means that 2 is an element of the set of numbers
  1,2,3
• 4 is not a member of that set

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How do you describe a set?

• If you have a set of numbers, there are two ways
  to describe the set
• Use a roster
• Use set-builder notation

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The Roster Method

• Just like in gym class when they read the roster,
  this simply lists all of the object in the set.
• Team A Andrews, Baxter, Jones, Smith, Wylie

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When to use a roster

• A roster works fine if you only have a few
  elements in the set.
• However, many sets of numbers are infinite.
• Listing each member would take the rest of your
  life!

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When to use a roster

• If an infinite set of numbers has a recognizable
  pattern, you can still use a roster.
• First establish the pattern
• then use an ellipsis
• to indicate that the pattern goes on
  indefinitely.
• 1, 2, 3, 4

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Set-builder notation

• For many infinite sets it is easier to just use a
  rule
• to describe the elements of the set.
• We use brackets to let everyone know that
  were talking about a set.
• We use a vertical line to mean such that
• lets see
  how it works

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Set-builder notation

• x x gt 0
• The set of all x such that x is positive.
• We couldnt possible use a roster to describe
  this set because it includes fractions and
  decimals as well as the counting numbers.
• We couldnt set up the pattern to begin with!

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Subsets

• Set A is a subset of set B if all of the members
  in set A are also in set B.
• set A 1, 2, 3 set B 1, 2, 3, 4, 5,
  6
• Set A is a subset of set B

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Subsets

• By definition, every set is a subset of itself.
• If set A has fewer elements than set B, it is
  called a proper subset and we use
• If they are the same set, it is called an
  improper subset and we use

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Union

• Two people get married (union) and merge their
  DVD collections. They sell all the duplicates on
  eBay the DVDs that are left are the union of
  their collections.
• all of hers all of his dups
• Lets look at a numeric
  example

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Union

• Set A 1, 2, 3 set B 3, 4, 5

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Intersection

• The intersection of Kirkwood and Walnut gets
  re-paved when Walnut get a facelift (because its
  part of Walnut) and it gets re-paved when
  Kirkwood get re-done (because its part of
  Kirkwood).
• The intersection of two sets are the elements
  that are members of both sets.

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Intersection

• Set A 1, 2, 3 set B 3, 4, 5

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The empty set

• Set A 1, 2, 3 set B 4, 5, 6
• There is no element that is in both sets, so the
  intersection is the empty set.

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The empty set

• The symbol for the empty set is the Greek letter
  Phi
• Do not put it in brackets.

is not empty. It is a set with one element
the Greek letter Phi
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Vocabulary
Element Subset Union Intersection Empty set