- #1
johnqwertyful
- 397
- 14
Homework Statement
We had to prove that an integral didn't exist by computing upper and lower sums. It was for
f(x)=x for rational
0 for irrational
Homework Equations
The Attempt at a Solution
Lower was easy, it's just 0 (inf of any interval is 0). But the upper I had a hard time with. I was trying to compute it for any arbitrary partition. Then I basically said that it's the same for f(x)=x, which works.
But the TA today said that the only partition that matters is the uniform one. That if we compute the upper sum for the uniform partition, it will be the inf of the upper sums.
Kind of my understanding of why is that as n->inf, the partition turns into a refinement of every single possible partition. Thus is the inf. Correct? Why even bother talking about other partitions then? If the uniform is the only one that matters...