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## Subtracting LUB and GLB to approach function

How do we know that the limit as n goes to infinity is 0?
Your tex isn't working either.

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 Quote by ArcanaNoir How do we know that the limit as n goes to infinity is 0?
Do you have a definition of an integral handy?

 Your tex isn't working either.
What????
My tex is beautiful!!!
What's wrong with it?
 Recognitions: Gold Member Yeah sorry.. My tex isn't working either. Which is weird because I'm on my iPad so it's not like I touched any settings. oh lovely on the definition of an integral. I see it is all there. Thanks, I will spend some time staring at that. Right after I figure out what happened to my tex... Thanks!
 Recognitions: Homework Help Perhaps I should add that those ##m_v## would define a set of narrow rectangles that are below the graph of f(x). That is, they would be a set of inscribed rectangles with height ##m_v##. The summed area of those rectangles approach the integral as the rectangles become narrower. This is the way the Riemann integral is defined.
 Recognitions: Gold Member Yeah I'm okay with how the sums are like integrals, I just wasn't sure how to get the difference between the upper and lower sums to be less than epsilon.