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### 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/

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