- #1
Gavins
- 27
- 0
Homework Statement
If b>a, find the infimum of b - a for arbritrary b,a.
Homework Equations
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The Attempt at a Solution
So this is for a darboux sum but I'm stuck on proving that 0 is the inf. It seems really easy but I can't seem to think straight.
First thing is 0 is a lower bound of b - a.
b - a > 0
b > a
Next is to prove it's the greatest lower bound. I tried to do this by supposing x > 0 is the greatest lower bound and find some contradiction but I can't figure it out.