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<p>every Interval  (thus, for all ). In modern mathematics, nested intervals are used as a construction method for the real numbers (in order to <a href="page.php?w=Complete_metric_space">complete</a> the <a href="page.php?w=Field_%28mathematics%29">field</a> of rational numbers).</p>

<p><big>Historic motivation</big></p>
<p>As stated in the introduction, historic users of mathematics discovered the nesting of intervals and closely related <a href="page.php?w=Algorithm">algorithms</a> as methods for specific calculations. Some variations and modern interpretations</p><p>
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