Difference between revisions of "Partition of an interval"
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− | A '''Partition of an interval''' is a way to formalise the intutive notion of ' | + | A '''Partition of an interval''' is a way to formalise the intutive notion of 'infinitesimal parts' of an interval. |
==Definition== | ==Definition== | ||
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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>. |
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+ | Where <math>x_{i-1}<t_i<x_i\forall t_i</math>. The points <math>t_i</math> are called the '''Tags'''. | ||
==See also== | ==See also== |
Revision as of 00:35, 16 February 2008
A Partition of an interval is a way to formalise the intutive notion of 'infinitesimal 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 .
Where . The points are called the Tags.
See also
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