>>25
"The limit does not exist ANYWHERE, and yet the function is defined EVERYWHERE."
What the hell? If a function is defined everywhere, then as x heads towards a particular number, the limit will easily evaluated.
ie. lim(x->1) (3x+5) = 8
"Take the unit step function for example."
Er. The reason why a limit does not exist is because the right hand limit, doesn't equal the left hand limit. This is the same case with asymptotes. When dividing by 0, the left hand limit equals +infinity, whilst the right hand limit equals -infinity.
"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."
True. When you take an inverse of a function, it's range and domain swap. Generally range becomes domain, vice versa.
Please read up on the Wikipedia link you suggested us.