I'm curious if you've taught calculus? Do your students remember limits by the end of calculus? Most studies show that students DO NOT RETAIN limit concepts (

I'm curious if you've taught calculus? Do your students remember limits by the end of calculus? Most studies show that students DO NOT RETAIN limit concepts (ESPECIALLY epsilon-delta ones). It is used as a crutch and then largely discarded before anyone is actually comfortable/familiar with them. By being a little handwavy at the beginning, you can then tell Dorothy that she's had her ruby slippers with her all along, and by this time they recognize the power and importance of the concept. In some ways, it is good to be able to explain, from the ground up, why each piece is in place. But, sometimes, understanding how to build a student requires knowing when we need to temporarily handwave something away so that it is actually meaningful when they get it. And then, doing that so they don't maintain a false conception is also important, which is why handwaviness is often helpful ("this is kind of like dividing by zero, but kind of not, and we will get to the distinctions later so just trust us for the moment").