Mathematical Induction
This appendix is a brief disussion of the topic, and is intended to be sufficient for the times in the book that a proof uses mathematical induction.
Suppose you are given a statement, S, that depends on a variable n; for instance,
Let n0 be the first value of n for which S applies, and prove the statement true. This is called the basis step. For our example, n0 = 1. Now, assume S is true for any n ≥ n0 and prove that this implies S is true for n + 1. This is called the inductive step.
Then,
• S is true for n0, so S is true for n1 = n0 + 1.
• S is true for n1, so S is true for n2 = ...
Get Numerical Linear Algebra with Applications now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.