Difference between revisions of "Partition of an interval"

Revision as of 01:31, 16 February 2008

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

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 $a=x_0<x_1<\ldots<x_n=b$

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

@@ Line 4: / Line 4: @@
 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}=\{x_0,x_1,\ldots,x_n\}</math> such that
+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>
@@ Line 13: / Line 13: @@
 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==