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Forum URL: http://www.cut-the-knot.org/cgi-bin/dcforum/forumctk.cgi
Forum Name: High school
Topic ID: 185
Message ID: 3
#3, RE: induction and function
Posted by sanjay on Aug-18-02 at 12:07 PM
In response to message #0
Induction generally can only be used on integer
arguments because the proof depends on a process
that hits every number. Keeping this in mind, here
is a general guideline that should assist you in
solving the induction problem above:

Firstly, make sure you know where you are
starting from. It is usually a good idea to
include both 0 and 1 in the base cases. (They
can be calculated by hand and then assumed in the
rest of the induction.)

f(0) = 0
f(1) = 1

In induction, we assume that we have already proved
that f(m) = m for all values of m <= k, and then
we prove that f(k+1) = k+1. This should help you
get started on your inductive proof.

Sanjay
Sanjay