Definition:Subdivision (Real Analysis)

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

Let $$x_0, x_1, x_2, \ldots, x_{n-1}, x_n$$ be points of $$\mathbb{R}$$ 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 $$\left[{a \,. \, . \, b}\right]$$.