>>24
"The very fact that it does not converge to a specific y-value, proves that it is impossibe to divide by zero."
Wrong. Limits have nothing to do with the actual value at a point. For example, take the piecewise function x = {1 if x is rational, 0 otherwise}. The limit does not exist ANYWHERE, and yet the function is defined EVERYWHERE. Convergence has nothing to do with whether or not the function is defined.
There are infinitely many examples of functions which are defined at points where the limit does not exist. Take the unit step function for example. Just like ordinary division, the limit does not exist at zero; it does not converge to a specific y-value. Yet it's still defined there. Its definition at zero has nothing to do with limits.
"Also, if you take an inverse of a function, you will effectively change its range and domain. Thereby your explaination with linear function is extremely inadequate."
How so? Alright, let me explain it with domain and range then. Multiplication of x by zero has the trivial range {0}, meaning the entire domain is in the kernel. This means it's not injective, hence it's not invertible. What did any of that have to do with limits? And what do higher polynomials or rational functions have to do with this?