![]() ![]() I strongly disagree pedagogically with the impulse behind "I would like to start my course with a beautiful example, not simply a basic function like 1/x."Įvery new crop of grain does not require a new sickle design. first half of the trip, half of the second half of the trip, etc. If you must (but see below) go with a life example, I think doing something like Zeno's paradox of motion might be helpful. Not complicated for us, but complicated for new-to-the-topic students. I feel like a lot of these suggestions are quite complicated. This is actually what I did, and I think the students got a better grasp of "what in god's name is happening?" than usual. ![]() In other words, you can lose some quality of approximation, but if the sequence converges, the quality of approximation will get as good as requested (and stay that good after that). The point is that a converging sequence might lose some quality of approximation locally, but over the time such losses (dropping below the certain quality threshold $\varepsilon$) must become impossible.
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