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PAGE UNDER CONSTRUCTION

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Primary reference: Chapter 1 (Sets) of Book of Proof by Richard Hammack

richardhammack.github.io

Content covered in this unit includes:

• Describing a set with set-builder notation or by listing its elements
• The idea that two sets are equal if and only if they contain the same elements
• The cardinality (or size) of a set, and the meaning of the terms finite and infinite
• The sets $\mathbb{N}$, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$
• The empty set $\varnothing = \{\}$, which contains no elements
• Intervals in the set of real numbers (open, closed, half-open, or infinite)
• The union and intersection of two or more sets, and the difference of two sets
• The complement of a set relative to some universal set
• The use of Venn diagrams to visually represent operations on sets (union, intersection, difference, complement)
• The definition of a subset of a set, and the power set of a set
• The definition of an ordered pair, and the Cartesian product of two setst