What is the worldwide mathmetician's view on 1/0?

Question

I recently asked my Maths teacher what he though 1/0 was. He told me it was infinity. I didn't beleive him but most other Maths teachers say the same thing. I can see why they could think this, since if you divide 1 by a smaller and smaller number the result increases. Since 0 is the smallest possible number, the result will be the biggest possible number, infinity.

However, most americans that I know (I'm english) think the opposite, they think the answer is either undefined or 0. I agree.

I would like to know the worldwide mathmetician's opinion on this matter, if there is one.

P.S. I've asked 'Dr Math'(google it) about this and it gave me no straight answer.

Answer 1

Technically, it is not infinity, but it approaches infinity. It is really undefined. (and, yes, I'm American)

Look at it this way. To prove 3 = 12/4, you multiply 4x3=12. But with 1/0, pretend it equals something and try to prove it. Let's say 1/0=A. Then A times 0 = 1. But we know that's not true. So, it's simply undefined. Can't do it!!!

that's it! :)

Answer 2

American here...

Either interpretation is valid.

In order to appreciate why 1/0 may be taken to represent infinity, consider what the operation of division does. To say, "divide a by b," is equivalent to asking the question, "what is the maximum number of times b can be subtracted from a before the remainder is less than a and greater than or equal to zero?" In the case that b=0 and a≠0, there is no limit to the number of times the subtraction can be performed. The VALUE of infinity is undefined.

Answer 3

It's undefined. 0/0 is a different story, where it depends on what's convenient for the situation, but 1/0 is generally gonna be considered undefined.

Answer 4

Division by zero is undefined. Division by a value that approaches zero approaches infinity. Lots of information at the link...