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.
You can't do it.
(Any attempt to define division by zero will "break arithmetic" somewhere.)
I am an algebraist, I define division to be multiplication by a reciprocal.
A reciprocal of
For any number,
In any ring whose additive identity is denoted
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.)