Difference between revisions of "Partition of an interval"
(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 ...) |
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Let <math>[a,b]</math> be an interval of real numbers | Let <math>[a,b]</math> be an interval of real numbers | ||
− | A '''Partition''' <math>\mathcal{P}</math> is defined as the ordered n-tuple of real numbers <math>\mathcal{P}= | + | A '''Partition''' <math>\mathcal{P}</math> is defined as the ordered n-tuple of real numbers <math>\mathcal{P}=(x_0,x_1,\ldots,x_n)</math> such that |
<math>a=x_0<x_1<\ldots<x_n=b</math> | <math>a=x_0<x_1<\ldots<x_n=b</math> | ||
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Let <math>\mathcal{P}=\{x_0,x_1,\ldots,x_n\}</math> be a partition. | Let <math>\mathcal{P}=\{x_0,x_1,\ldots,x_n\}</math> be a partition. | ||
− | A '''Tagged partition''' <math>\mathcal\dot{P}}</math> is defined as the set of ordered pairs <math>\mathcal\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n</math>. The points <math>t_i</math> are called the '''Tags'''. | + | A '''Tagged partition''' <math>\mathcal{\dot{P}}</math> is defined as the set of ordered pairs <math>\mathcal{\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n</math>. The points <math>t_i</math> are called the '''Tags'''. |
==See also== | ==See also== |
Revision as of 00:31, 16 February 2008
A Partition of an interval is a way to formalise the intutive notion of 'infinetesimal parts' of an interval.
Contents
[hide]Definition
Let be an interval of real numbers
A Partition is defined as the ordered n-tuple of real numbers such that
Norm
The Norm of a partition is defined as
Tags
Let be a partition.
A Tagged partition is defined as the set of ordered pairs . The points are called the Tags.
See also
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