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### Division of Number Line

```
Date: 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

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/
```
Associated Topics:
Middle School Algebra

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