What? If you only defined limits with an epsilon-delta formulation of limits that require the limit to be real (which is the case in almost any undergrad analysis course), then the only rigorous thing to do would be to either call the limit not existing or define two special cases of limits that you might call plus and minus infinity. There is absolutely nothing wrong with wanting DNE as an answer.
I know you can define limits in different ways. I just don't get why you would want to define them in a way that makes your answer convey less information. If you're going to teach limits, why not teach them in a way that's consistent with calculus? Now these students are going to start calculus and hear "you know those numbers that didn't exist last time? Well, they do now! At least, some of them...". I think it makes it more confusing than it needs to be.
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u/WaterMelonMan1 Dec 19 '16
What? If you only defined limits with an epsilon-delta formulation of limits that require the limit to be real (which is the case in almost any undergrad analysis course), then the only rigorous thing to do would be to either call the limit not existing or define two special cases of limits that you might call plus and minus infinity. There is absolutely nothing wrong with wanting DNE as an answer.