Since is going to be going to we can consider only those 's closer to than - that is all this is saying

You want to get a bound that gets rid of the term in the denominator, so you find the minimum value of when and use that in place of the to give an upper bound.Then this is where I really get confused:

Q: Where did they get this from? I understand that it is less than that, but I don't get how they got that. Like if I were doing a different problem, would I just pull that out of thin air?

There is no unique way of proceeding with these things, what you do is you play around with vaules to find ones that work. You have:Then they say we may take

Q: I kind of understand this, so that it will always be less than , but I'm again not sure where they got this?

If anyone could help me, that would be awesome. I really want so badly to understand how to do this, I just can't do it alone!

Thank you.

so now you need to find a when is close to .

CB