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Set Theory

Set Theory. Using Mathematics to Classify Objects. The Language of Sets. 2.1. Specify sets using both listing and set-builder notation Understand when sets are well-defined Use the element symbol property. ( continued on next slide ). The Language of Sets. 2.1.

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Set Theory

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  1. Set Theory Using Mathematics to Classify Objects

  2. The Language of Sets 2.1 • Specify sets using both listing and set-builder notation • Understand when sets are well-defined • Use the element symbol property (continued on next slide)

  3. The Language of Sets 2.1 • Find the cardinal number of sets

  4. Representing Sets • Set – collection of objects • Element – a member of a set

  5. Representing Sets • Set-builder notation:

  6. Representing Sets • Set – collection of objects • Element – a member of a set • Set-builder notation:

  7. Representing Sets • A set is well-defined if we are able to tell whether any particular object is an element of the set. • Example: Which sets are well-defined? (a) (b)

  8. Representing Sets • Do  and {} mean the same thing? •  is the empty set – a set with no members • {} is a set with a member object, namely, the empty set

  9. Representing Sets • Example: Consider female consumers living in the U.S. The universal set is

  10. The Element Symbol • Example:

  11. Cardinal Number • Example: State the cardinal number of the set.

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