Set Theory

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.