Definition:Subdivision

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Definition

Let $\left[{a .. b}\right]$ be a closed interval of the set $\R$ of real numbers.

Let $x_0, x_1, x_2, \ldots, x_{n-1}, x_n$ be points of $\R$ such that:

$a = x_0 < x_1 < x_2 < \cdots < x_{n-1} < x_n = b$

Then $\left\{{x_0, x_1, x_2, \ldots, x_{n-1}, x_n}\right\}$ form a subdivision of $\left[{a .. b}\right]$.

Some sources use the term partition for this, but the latter term has an alternative and more general definition so it is probably better not to use it.