Let
Suppose you want to show f is a continuous function for all x.
Since function f is continuous at a if
and a function is continuous on its domain if the above holds for all x in the domain, one could say:
Therefore the function f is continuous.
My professor scratched his head for moment before agreeing it made sense, so I'm guessing there's a more conventional form for expressing this idea. What is it, I can't wait for my next class.