# Math Help - mesh

1. ## 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 $||\pi|| = \min\limits_{1 \leq i \leq n} \Delta x_i$?

2. Originally Posted by heathrowjohnny
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.