Commit 27b53632 authored by Jim Hefferon's avatar Jim Hefferon

add that initial induction number may be a small list

parent 934bc5ce
......@@ -371,7 +371,7 @@ This section is a pause for an introduction to induction.
We will start with exercises about summations.
(However, note that induction is not about summation;
we start with these simply because they make good initial exercises.)
we start with these simply because they make good exercises.)
For example, in playing with numbers
many people have noticed that the odd natural numbers sum to
perfect squares: $1+3=4$, $1+3+5=9$, $1+3+5+7=16$, etc.
......@@ -388,9 +388,10 @@ natural number variable.
These proofs have two steps.
For the \definend{base step}
we will show that the statement holds for some intial number~$i\in\N$.
we will show that the statement holds for some intial number~$i\in\N$
(sometimes there is a finite list of initial numbers).
The \definend{inductive step} is more subtle;
we will show that the following implication holds.
we show that the following implication holds.
\begin{equation*}
\begin{tabular}{l}
If the statement holds from the
......@@ -681,7 +682,7 @@ While many induction arguments use only the the $n=k$ part of the inductive
hypothesis,
some break from that pattern.
\begin{problem}
\begin{problem} % Replace with proof that every number is a product of primes?
The game of Nim starts with two piles, each containing $n$~chips.
The two players take turns picking a pile and removing
some nonzero number of chips.
......
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