Apologies if this has been asked somewhere else. Why do we say $f(x) = \frac{x^2}{x}$ is undefined at 0 when it literally equals $f(x) = x$. Am I making a mistake in saying that $\frac{x^2}{x} = x$?
Indeed why does any function with a removable discontinuity, such as $\frac{x-2}{x^2-4}$ (which can be rewritten as $\frac{1}{x+2}$) actually "have" the discontinuity if we can always rewrite it in some way which makes the limit easy to evaluate?
