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Q&A #3893

Teachers' Lounge Discussion: Dividing by zero

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From: Tim Payer <tsp1@humboldt.edu>
To: Teacher2Teacher Public Discussion
Date: 2002121017:45:57
Subject: Division by Zero

	Hello,

Here is what I give to my students as to why division by zero is
undefined.
First we recognize that to divide by anything we are talking about a
fraction or a rate. The most common rate we deal with every day is
that of speed. Draw a positive sloped line to represent a speed of 55
miles per hour. Of course hardly anyone still travels at 55 miles per
hour, so lets make the line steeper to show the more common freeway
speed of 75 miles per hour. We can make this line even steeper to
reflect the speed of light: 186,000 miles per second. But the point is
that even at this fantastic rate of speed, the ratio of distace to
time is held constant. We can determine that at a given distance d, to
say a given planet, it will take so many seconds to reach the planet.
Now, sketch the steepest of lines: a vertical line. What has happened
to your rate of speed now? What has happened to your slope?
What is your rise and run? How long does it take one to reach New York
city, Or Tokyo or the far reaches of the Gamma Quadrant? 
It takes no time at all! We are already there, at all locations
simultaneously. WHAT IS GOING ON HERE?
    We are describing something but it is more of an idea or concept,
not a rate of speed. We can't multiply this by 2. We can't take the
square root of being everywhere simultaneously. So we aknowledge that
we have described something but as far as math is concerned we CAN'T
USE THIS. We put this idea on a shelf as "UNDEFINED".

                             Tim Payer, HSU Math Dept.

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