Division of Number LineDate: 5/14/96 at 17:31:34 From: Anonymous Subject: Division of number line Using the number line, more specifically the interval from zero to one, how do I explain that when you find half the distance and then half of that distance and so on, you'll never settle on one number? Date: 5/17/96 at 19:13:17 From: Doctor Ken Subject: Re: Division of number line Hello - Here's one way you can do it. You start out with distance 1. At the next step, you have distance 1/2. Then 1/4, 1/8, and so on. Notice that at each step, if the distance from one step was x, then the distance at the next step is x/2. Now, if x is positive, then x/2 is also positive and - here's the main point - x/2 isn't equal to x (you can show this with inequalities - start with x > 0). So if you know that at each successive step you get a different number than you had at the last step, that means you won't settle on one number. -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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