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Math Help - Partitions

  1. #1
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    Exclamation Partitions

    Let [a,b] \rightarrow{}\mathbb{R} a bounded fuction.

    Prove that if P_1 and P_2 are partitions of [a,b] then:

    L(P_1,f) \leq{U(P_2,f)}

    Thanks a lot
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  2. #2
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    Quote Originally Posted by osodud View Post
    Let [a,b] \rightarrow{}\mathbb{R} a bounded fuction.
    Prove that if P_1 and P_2 are partitions of [a,b] then: L(P_1,f) \leq{U(P_2,f)}
    To do this you need to understand a refinement of a partition.
    Prove that if  Q' is a refinement of the partition Q then
    L(Q,f) \leqslant L(Q',f) \leqslant U(Q',f) \leqslant U(Q,f) .

    Then to do your problem find a refinement of P_1\cup P_2.
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