Yes.If delta < epsilon/2?
I have been out of college math teaching for about 13 years now, so I haven't really been following calculus textbooks much. Different books seemed to take different approaches with regard to how rigorously limits were presented. I don't believe that high school texts do much in the way of epsilon-delta presentations of limits, but then I haven't seen any high school texts for a good long while.Hi
I don't think I'll go on to trickier problems :)
I just want to learn a bit of the proof behind some of the calculus I am learning as I feel a bit uncomfortable applying things without knowing where they come from. If I understand how the basic examples are done, I can feel comfortable the more complex examples can be prooved without knowing how to do them myself.
I'm from the UK and even in the calculus books i have for school/college level (up to 18 years old) they don't mention really touch on the theory of limits; they give an intuitive idea of what a limit is and then just dive straight in with differentiation and integration. The books I have now are american and have quite a different approach. Do you study this sort of thing at school/college in america? It seems in the UK you don't do it until university.