Editing Partition of an interval (section)

{{Short description|Increasing sequence of numbers that span an interval}}
{{about|grouping elements of an interval using a sequence|grouping elements of a set using a set of sets|Partition of a set}}

[[File:Integral Riemann sum.png|thumb|300px|A partition of an interval being used in a [[Riemann sum]]. The partition itself is shown in grey at the bottom, with the norm of the partition indicated in red.]]

In [[mathematics]], a '''partition''' of an [[interval (mathematics)|interval]] {{math|[''a'', ''b'']}} on the [[real line]] is a finite [[sequence]] {{math|''x''<sub>0</sub>, ''x''<sub>1</sub>, ''x''<sub>2</sub>, …, ''x<sub>n</sub>''}} of [[real number]]s such that

:{{math|''a'' {{=}} ''x''<sub>0</sub> < ''x''<sub>1</sub> < ''x''<sub>2</sub> < … < ''x''<sub>''n''</sub> {{=}} ''b''}}.

In other terms, a partition of a [[compact space|compact]] interval {{mvar|I}} is a strictly increasing sequence of numbers (belonging to the interval {{mvar|I}} itself) starting from the initial point of {{mvar|I}} and arriving at the final point of {{mvar|I}}.

Every interval of the form {{math|[''x''<sub>''i''</sub>, ''x''<sub>''i'' + 1</sub>]}} is referred to as a '''subinterval''' of the partition ''x''.