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AND. Chapter 2 . Sets. • Methods to indicate sets, equal sets, and equivalent sets • Subsets and proper subsets • Venn diagrams • Set operations such as complement, intersection, union, difference and Cartesian product • Equality of sets • Application of sets • Infinite sets.

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  1. AND

  2. Chapter 2 Sets

  3. • Methods to indicate sets, equal sets, and equivalent sets • Subsets and proper subsets • Venn diagrams • Set operations such as complement, intersection, union, difference and Cartesian product • Equality of sets • Application of sets • Infinite sets WHAT YOU WILL LEARN

  4. Section 6 Infinite Sets

  5. Infinite Sets • An infinite set is a set that can be placed in a one-to-one correspondence with a proper subset of itself. • These sets are “unbounded”.

  6. Example: The Set of Multiples of Four Show that it is an infinite set. {4, 8, 12, 16, 20, …,4n, …} Solution: We establish one-to-one correspondence between the set and a proper subset of itself. Given set: {4, 8, 12, 16, 20, …, 4n, …} Proper subset: {8, 12, 16, 20, 24…, 4n + 4, …} Therefore, the given set is infinite.

  7. CourseSmart Page 93

  8. Countable Sets • A set is countable if it is finite or if it can be placed in a one-to-one correspondence with the set of counting numbers. • Any set that can be placed in a one-to-one correspondence with a set of counting numbers has cardinality aleph-null and is countable.

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