Explaining Mathematical Induction

Date: 08/29/98 at 11:23:16
From: kate caruselle
Subject: Induction

I have to do a report and the math article involves mathematical 
induction. I have not yet learned this and wanted to know what 
mathematical induction is.

Date: 08/29/98 at 12:11:25
From: Doctor Barrus
Subject: Re: Induction

Hi, Kate.

Mathematical induction is one way mathematicians prove things. What it 
is, basically, is this:

Let's say I wanted to prove something about numbers.

Step 1: First I would show that this statement is true for the 
        number 1.

Step 2: Next, I would show that if the statement is true for one 
        number, then it's true for the next number.

These two steps complete a proof. It's kind of like dominoes. If you 
want to knock down all the dominoes you have, they all have to be lined 
up in the right way (so that they'll knock each other over), and you 
have to be able to knock the first domino down (so that all the others 
will fall). Well, showing that your statement is true for 1 is like 
making sure you can knock down the first domino. Proving that if your 
statement is true for one number, then it's true for the next, is like 
making sure all the dominoes are lined up correctly, meaning that when 
one falls down, it will knock down the next one. When you put these 
things together - everything's lined up and you can knock down the 
first one - you've proved that you can knock down all the dominoes, or 
that your statement is true for all positive whole numbers.

I hope that's understandable. But basically, mathematical induction is 
just a way of proving things about numbers.

Hope this helps. If you have any more questions, feel free to write 
back. Good luck on your report!

- Doctor Barrus, The Math Forum
Chekc out our web site! http://mathforum.org/dr.math/