What is 1 divided by 0... Type it on the calculator and you get a "Math error" Anyone got an answer?

Answer 1

division by zero is undefined.

you cannot have a real number say X such that
0 * X = 1

Answer 2

There are several good explanations already, but there are some misleading ones too. 1/0 does not equal infinity. Look at it this way.

The function f(x)=1/x on the domain of the real numbers has an essential (i.e. not removable) discontinuity at 0. This means there is no way to give f(0)=1/0 a real value and make 1/x continuous over the reals.

Sometimes people suggest that we define f(0)=1/0 as infinity. This fails for two reasons, one practical and one technical.
i) The limit from the left is negative infinity, not infinity. So f(x) is still discontinuous at 0. Sorry.
ii) Infinity is not a real number. If we include infinity in the range of f(x), then f maps the real numbers to the "extended real numbers". This means it's a different function, and that defeats the purpose of trying to plug the gap in our original function.

The point: 1/0 does NOT equal infinity.

Answer 3

1 divided by 0 is not well-defined (that is, it doesn't have an answer that makes mathematical sense). You cannot divide by zero, because otherwise, if 1/0=x, for example, then it would be true that 1 = 0*x, because you could multiply through by 0. But that's impossible, because 0 times anything has to be zero. That is why division by zero is always explicitly prohibited.

Answer 4

This is an interesting question, actually. Usually when we have a set of numbers and an operation, we ask whether the set of numbers is "closed" for that operation. I.e., integers are closed for addition - the sum of any two integers is another integer. Similarly for multiplication - the product of any two integers is another integer. Only division throws a wrench in the works - e.g. 1/2 is not an integer. We might instead suppose that division is closed for rational numbers, but as you point out, zero is a problem.

The usual answer to "what is 1/0" is "infinity" (it is wrong to say it is "undefined" - that's usually reserved for more perplexing questions like "what is 0/0"). Now, whether we accept the validity of this premise is dependent on (a) whether we demand closure in the operation (multiplication and division are closed on non-zero rational numbers, but not on all rational numbers) and (b) whether we consider infinity to be a number. This is a simple matter of definition, in fact, and is long-debated. Here is a page with some arguments on the subject:
http://www.johnath.com/~david/etc/infinity.html

Also try this one, for a discussion of the mathematics of infinity:
http://scidiv.bcc.ctc.edu/Math/Infinity.html

EDIT: Ah, kudos to thefreevariable who points out the obvious fact that the 1/0 is infinity from the right and -infinity from the left. Duh. Give him +10!

Answer 5

1/0 is a non-answer.

It shows as an error because you cannot divide ANYTHING by zero.

Basic math principle you should have learned in the 3rd grade.

Answer 6

The best approximation for division by zero is to divide by a very small number. i.e. 1/0.000000000000000000001 etc. If you keep making this number smaller and smaller, the result will get larger. It will eventually approach infinity. So 1/0 = infinity.

Answer 7

You can divide anything by zero, it's not physically possible. So you can't really get an answer.
Look at it like this:
Imagine you have 4 divided by 2
There are four things:
* * * *
And two people to share them between: @ @

So each person get two, right? @ * * @ * *

But with 1 divided by 0 you have this
I thing to share :
*
But no one to give it to show you can't so really its not there, but it is so therefore it is a Math Error as it's not possible to get an answer.

But if you desperatly needed an answer use that ^ but put it simpler or put it, more incorrect, but you could put it as zero.

Answer 8

There is nothing that you can divide zero by and get one!!! That's the same as getting something from nothing. Think of it as this way: What times zero equal one? Error! Can't happen!

Answer 9

Division by 0 is not meaningful. As one divides by smaller and smaller numbers, approaching 0, the result approaches infinity (positive or negative, depending upon signs of numerator and denomenator). This discussion relates to the "limit" concept.

Answer 10

1 / 0 is undefined because there is no number multiply by
0 gives 1