Explaining Mathematical InductionDate: 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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