8: Appendices
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- 8.1: Sets and Set Notation
- A set is a collection of things called elements. For example {1,2,3,8} would be a set consisting of the elements 1,2,3, and 8. To indicate that 3 is an element of {1,2,3,8}, it is customary to write 3∈{1,2,3,8}. We can also indicate when an element is not in a set, by writing 9∉{1,2,3,8} which says that 9 is not an element of {1,2,3,8}. Sometimes a rule specifies a set.
- 8.2: Well Ordering and Induction
- This page introduces summation notation and its applications, emphasizing well-ordered sets and mathematical induction. It explains how summation notation provides a concise representation of sums and describes the principle of well-ordering underlying induction. The section outlines the induction process, including base cases and steps, illustrated by examples that prove formulas and inequalities for all natural numbers.