Subtracting LUB and GLB to approach function

ArcanaNoir

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

I like Serena

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?

ArcanaNoir

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!

I like Serena

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.

ArcanaNoir

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.

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ArcanaNoir Recognitions: Gold Member	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.

I like Serena 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.