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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