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Math Help - mesh

  1. #1
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    mesh

    In the definition of the Riemann integral we choose a partition of an interval as follows:  \pi = \{a = x_{0} < x_{1} < \cdots < x_{n} = b \} and set  \Delta x_i = x_i - x_{i-1} .

    Then we define the mesh as  ||\pi|| = \max\limits_{1 \leq i \leq n} \Delta x_i . So is this the maximum distance  \Delta x_i ?

    Why not define it as  ||\pi|| = \min\limits_{1 \leq i \leq n} \Delta x_i ?
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  2. #2
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    Quote Originally Posted by heathrowjohnny View Post
    Why not define it as  ||\pi|| = \min\limits_{1 \leq i \leq n} \Delta x_i ?
    Because it is not useful. Knowing the maximum is what is useful in doing proofs involving the integral.
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