My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news

LinkBack Thread Tools Display Modes
November 28th, 2017, 10:51 AM   #1
Joined: Oct 2017
From: Rumba

Posts: 39
Thanks: 0

Proof by induction

Would i be ok to use base step as n = 1 for a function A -> B for one in A

A (x) mapping to B (a1,a2,a3.... am)

No of functions possible for n-1 is m^n

I dont know how to go on with the induction step any ideas?

Last edited by sita; November 28th, 2017 at 10:57 AM.
sita is offline  
November 28th, 2017, 11:05 AM   #2
Senior Member
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

To prove by weak mathematical induction the proposition

$P(n) \text { is true for any } n \in \mathbb N^+$,

first prove $P(1) \text { is true.}$ This is frequently very easy to do.

Moreover it justifies the following statement:

$\exists \text { at least one number } k \in \mathbb N^+ \text { such that } P(k) \text { is true.}$

This is frequently called the assumption step although it is clearly a true statement. Notice however, that you may NOT assume that k = 1. You may assume that $k \ge 1.$

Now prove in the second step that

$P(k + 1) \text { is true.}$

What is the intuition?

P(1) is true by the first step so P(1 + 1) = P(2) is true by the second step, so P(2 + 1) = P(3) is true by the second step, so P(3 + 1) = P(4) is true by the second step, and so on forever.

Last edited by JeffM1; November 28th, 2017 at 11:08 AM.
JeffM1 is offline  

  My Math Forum > Math Forums > Math

induction, proof

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Proof by induction Jimi Algebra 2 March 10th, 2014 06:41 AM
proof by induction walter r Calculus 3 April 26th, 2013 04:25 AM
Proof by induction 3,14oner Abstract Algebra 4 April 11th, 2012 12:37 AM
proof by induction Airmax Applied Math 9 May 8th, 2009 12:02 PM
proof by induction MaD_GirL Number Theory 5 November 14th, 2007 06:34 PM

Copyright © 2019 My Math Forum. All rights reserved.