Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

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 
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/   
    
Associated Topics:
Middle School Algebra

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/