Partition of an interval

Revision as of 00:28, 16 February 2008 by Shreyas patankar (talk | contribs) (New page: A '''Partition of an interval''' is a way to formalise the intutive notion of 'infinetesimal parts' of an interval. ==Definition== Let <math>[a,b]</math> be an interval of real numbers ...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

A Partition of an interval is a way to formalise the intutive notion of 'infinetesimal parts' of an interval.

Definition

Let $[a,b]$ be an interval of real numbers

A Partition $\mathcal{P}$ is defined as the ordered n-tuple of real numbers $\mathcal{P}=\{x_0,x_1,\ldots,x_n\}$ such that $a=x_0<x_1<\ldots<x_n=b$

Norm

The Norm of a partition $\mathcal{P}$ is defined as $\|\mathcal{P}\|=\sup\{x_i-x_{i-1}\}_{i=1}^n$

Tags

Let $\mathcal{P}=\{x_0,x_1,\ldots,x_n\}$ be a partition.

A Tagged partition $\mathcal\dot{P}}$ (Error compiling LaTeX. Unknown error_msg) is defined as the set of ordered pairs $\mathcal\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n$ (Error compiling LaTeX. Unknown error_msg). The points $t_i$ are called the Tags.

See also

This article is a stub. Help us out by expanding it.