Proof that Upper Riemann Integral > Lower Riemann Integral...?
im new at this level of maths so i would appreciate a lil bit of help here and there :) hehe
i want to show that
lower riemann integral upper riemann integral
i have worked this out so far but im not sure if its correct: please help me on my solution.
if P,Q are partitions of P[a,b] (i.e P,Q P[a,b] then
If we let R:=P U Q, be a common refinement of P & Q then we see that:
L(f,P) L(f,R) &
We know L(f,R) U(f,R) so now,
L(f,P) L(f,R) U(f,R) U(f,Q)
This deduces that L(f,P) U(f,Q).
sup L(f,P) inf U(f,P).... which is the same as
lower riemann integral < upper riemann integral..
Is this proof totally correct? or is there another solution to proving this? thanks a lot :) xxx