Ok so firstly, I'm not entirely sure where this thread should land so it's going in here lol. So this question is inspired by doing preliminary algebra on a function in order to find a limit that initially results in an indeterminate form. What does it say about what we get from the face value of a written equation, and what it actually is? For example, lim x→1 of (x^2 - 1) / (x - 1) makes the exact same looking graph on a calculator as (x-1) , but the first equation does not exist at 1, whereas the second one does! BLLAAAARRGGHHHHH!!!!!