Upper and Lower sums – Riemann Integral

If P1 and P2 are partitions of [a,b] such that P1 âٹ‚ P2 then it follows that:

L(P1) ≤ L(P2) and U(P1) ≥ U(P2)

can someone maybe explain why this is true intuitively or graphicly 😀 tx guys much appreciated

=================

  

 

Can you clarify your notation?
– Armando j18eos
2 days ago

  

 

i do apologize I’m kind of new to this I will update my question so that it’s more clear
– Anrich
2 days ago

  

 

Here’s a starting point: can you see why this is true when P1={a,b}P_1 = \{a,b\} (that is, we didn’t partition the interval at all!) and P2={a,x1,b}P_2 = \{a,x_1,b\} (so a single interior partition point splits the interval into two subintervals)?
– Greg Martin
2 days ago

  

 

Yes! thank you seeing it that way makes it a lot easier…. I was a bit fuzzy about the subset meaning but now I see that they basically mean is the one set has more sub intervals (or points) then the other….when i think of it that way this seems pretty straight forward 🙂
– Anrich
2 days ago

=================

=================