Category:Subdivisions (Real Analysis)

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This category contains results about subdivisions in the context of Real Analysis.
Definitions specific to this category can be found in Definitions/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 $\closedint a b$.

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