Which comes back to the problems with the OPs argument. Sure, you can explain continuity in a few simple sentences but sooner or later you will start to hit corner cases and you find that those few simple sentences are really quite ambiguous. It's much like using pseudocode to describe an algorithm. I've found that the best mathematical texts provide both - a 'morally correct' definition in plain english to describe the intention and a mathematical description which defines the precise meaning.