# Question #d0dfe

##### 2 Answers

When you divide, say,

But this number

But this is not possible!

So, it is not possible to divide by

On the other hand have a look at what happens if you get "near" to zero but not zero.

Try

You can't do it.

(Any attempt to define division by zero will "break arithmetic" somewhere.)

**Reason 1**:

But if

(For example:

**Reason 2**:

I am an algebraist, I define division to be multiplication by a reciprocal.

A reciprocal of

For any number,

**(General case)**

In any ring whose additive identity is denoted

we have

So the only ring in which

(The trivial ring has one thing in it. That thing is the additive and multiplicative identities. In non-trivial rings, it is not possible for both identities to be the same.)