Skip to main content

# 2: Induction and Recursion

• Page ID
6099
•

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

If you are unfamiliar with the Principle of Mathematical Induction, you should read Appendix B. The principle of mathematical induction states that In order to prove a statement about an integer $$n$$, if we can 1. Prove the statement when n = b, for some fixed integer b, and 2. Show that the truth of the statement for $$n = k − 1$$ implies the truth of the statement for $$n = k$$ whenever $$k > b$$, then we can conclude the statement is true for all integers $$n ≥ b.$$

Thumbnail: A drawing of a graph. Image used with permission (Public Domain; AzaToth).