Category:Definitions/Subdivisions (Real Analysis)

This category contains definitions related to subdivisions in the context of Real Analysis.
Related results can be found in Category:Subdivisions (Real Analysis).

Let $\closedint a b$ be a closed interval of the set $\R$ of real numbers.

Finite

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 $\set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ form a finite subdivision of $\closedint a b$.

Infinite

Let $x_0, x_1, x_2, \ldots$ be an infinite number of points of $\R$ such that:

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

Then $\set {x_0, x_1, x_2, \ldots}$ forms an infinite subdivision of $\closedint a b$.