- #1
TheyCallMeMini
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Homework Statement
Suppose f is a function bounded on [a,b], A=GLB(S u,f), and B=LUB(S W,f).
Homework Equations
1. For each e>0, there is a subdivision D={Xi}of [a,b] such that |U f,D - W f,D|<e
2. There is a number Q such that if e>0, then there is a subdivision D of [a,b] such that if K={Yi}is a refinement of D, then |U f,K - Q|<e and |W f,K - Q|<e.
U=upper sums
W=lower sums
The Attempt at a Solution
I'm supposed to show that 1 implies 2 and 2 implies 1. Trying to do 1 implies 2 confuses the hell out of me, but if I do 2 implies 1 isn't that just doing a triangle inequality and account for the number Q?