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In mathematics, a partition of an interval (''b'' ) on the real line is a finite sequence ''x = ( xi )'' of real numbers such that :''a'' = ''x''0 < ''x''1 < ''x''2 < ... < ''x''''n'' = ''b''. In other terms, a partition of a compact interval ''I'' is a strictly increasing sequence of numbers (belonging to the interval ''I'' itself) starting from the initial point of ''I'' and arriving at the final point of ''I''. Every interval of the form (''x''i+1 ) is referred to as a sub-interval of the partition ''x''. ==Refinement of a partition== Another partition of the given interval, ''Q'', is defined as a refinement of the partition, ''P'', when it contains all the points of ''P'' and possibly some other points as well; the partition ''Q'' is said to be “finer” than ''P''. Given two partitions, ''P'' and ''Q'', one can always form their common refinement, denoted ''P'' ∨ ''Q'', which consists of all the points of ''P'' and ''Q'', re-numbered in order. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Partition of an interval」の詳細全文を読む スポンサード リンク
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