# zero

#### messa

##### New member
Hello, My question is:

Sue argued that 0/0=1 because any number divided by itself is 1. What would you tell her?

I was thinking that the zero property says that any number didvided by zero is undefined. But I think the question is asking for more than that. Could someone please help me here?

#### ting

##### Junior Member
"Thou shalt not divide by zero!"

From

0/0 = 1

You get

1 * 0 = 0

and

0/1 = 0

Both of which are true.

So you'd try to convinve sue that dividing by zero is a bad idea, period.

Mutiplying by a number cancels dividing by it, so multiplying by zero should undo dividing by zero, which it does not!

(1/0) * 0 = 1 Not true, multiply by zero and you get zero

or just ask her to leave the class!

Google will give you lots of info on dividing by zero, here is a couple of links.

http://mathforum.org/t2t/discuss/messag ... =3893&n=16

http://mathforum.org/dr.math/faq/faq.divideby0.html

#### Matt

##### Junior Member
messa said:
Hello, My question is:

Sue argued that 0/0=1 because any number divided by itself is 1. What would you tell her?
Any fraction with a 0 in the numerator is 0. For example, 0/143=0. Thus 0/0=0.

#### stapel

##### Super Moderator
Staff member
We have three possible interpretations:

. . . . .1) 0/m = 0 for all m other than 0.

If we allow m = 0, then 0/0 = 0.

. . . . .2) m/m = 1 for all m other than 0.

If we allow m = 0, then 0/0 = 1.

. . . . .3) m/0 is undefined for all m other than 0.

If we allow m = 0, then 0/0 is undefined.

Hence, "0/0" is an "indeterminant" expression. It may have a defined interpretation within certain contexts, but my understanding is that, at the moment, "0/0" has no fixed, across-the-board interpretation, and is, in general, to be avoided.

Eliz.