Can You Have Zero in the Denominator?

From: Anonymous
Subject: Math of course! :)
Date: Mon, 07 Nov 1994 19:58:42 EST

        Hi! My name is Emma Stickgold -not matilda.. :) - and I have been
asked to ask you a question. My math teacher, Steve Barkin at the Graham
and Parks school in Cambridge, MA, and I are in the midst of an argument
over whether any number can be placed over zero in a fraction. I know
that when you take a fraction like 10/5, it equals 2, and 5 * 2 = 10, and
that works out for all fractions where the numerator is larger than the
denominator, but it doesn't work out for n/0. 

        I know that you'll probably say that it isn't a legit. fraction, but...
 I still say that it is. :)

        Please send me your opinion ASAP... :)
            Yours,
             a seventh grader in the midst of an argument w/math teacher,
                Emma

Date: Mon, 7 Nov 1994 20:22:46 -0500 (EST)
From: "Michael W. S. Morton"

Hello Emma!

I'm Mike, one of the Math Doctors here....

I can't really give you a great reason why you can't put 0 in the 
denominator of a fraction, but I'll give you something to think about 
while another Math Doctor comes up with a better answer!!

Try thinking about this:
what is:
        10/1 = ?
        10/.5 = ?
        10/.1 = ?
        10/.01 = ?
        10/.00001 = ?
        10/.0000000000001 = ? 

You can see that as the denominator becomes very small, the fraction 
becomes very large.  As you approach 0 in the denominator, the 
fraction becomes HUGE!  If the denominator was to equal 0, we might 
say that the fraction was INFINITE!!  That is, it is bigger than ANY 
number you can think of!  That is usually the reason I think of when I 
want to put 0 in the denominator of a fraction.  

If you don't understand that, or if you want a better explanation, please 
write back!
                                                -MORTON, Doctor of sorts

From: Anonymous
Date: Sat, 23 Nov 1996 21:47:46
Subject: Idea on explaining something

I noticed that one of your math doctors was having trouble 
explaining to a girl named Emma back in '94 why zero can't be the 
numerator or denominator in fraction.  Well, if you're still 
looking for a good way to explain it, my math teacher uses the 
example "How many times can you throw nothing into no 
wastebaskets?"  And of course the answer is as many times as you 
want.  It's just not a real number.  

Hope I was of some help,

                                  Geri