https://number.subwiki.org/w/index.php?action=history&feed=atom&title=Strict_minimum-so-farStrict minimum-so-far - Revision history2026-05-04T23:00:51ZRevision history for this page on the wikiMediaWiki 1.41.2https://number.subwiki.org/w/index.php?title=Strict_minimum-so-far&diff=281&oldid=prevVipul at 18:39, 2 May 20092009-05-02T18:39:59Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:39, 2 May 2009</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Definition==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>f</math> is an arithmetic function from the [[natural number]]s to a subring of the ring of real numbers. Then, a [[natural number]] <math>n</math> is termed a '''minimum-so-far''' for <math>f</math> if <math>f(n) < f(m)</math> for all natural numbers <math>m < n</math>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>f</math> is an arithmetic function from the [[natural number]]s to a subring of the ring of real numbers. Then, a [[natural number]] <math>n</math> is termed a '''<ins style="font-weight: bold; text-decoration: none;">strict </ins>minimum-so-far''' for <math>f</math> if <math>f(n) < f(m)</math> for all natural numbers <math>m < n</math>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Related notions==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>==Related notions==</div></td></tr>
</table>Vipulhttps://number.subwiki.org/w/index.php?title=Strict_minimum-so-far&diff=280&oldid=prevVipul: Created page with '==Definition== Suppose <math>f</math> is an arithmetic function from the natural numbers to a subring of the ring of real numbers. Then, a natural number <math>n</math> ...'2009-05-02T18:39:20Z<p>Created page with '==Definition== Suppose <math>f</math> is an arithmetic function from the <a href="/w/index.php?title=Natural_number&action=edit&redlink=1" class="new" title="Natural number (page does not exist)">natural numbers</a> to a subring of the ring of real numbers. Then, a <a href="/w/index.php?title=Natural_number&action=edit&redlink=1" class="new" title="Natural number (page does not exist)">natural number</a> <math>n</math> ...'</p>
<p><b>New page</b></p><div>==Definition==<br />
<br />
Suppose <math>f</math> is an arithmetic function from the [[natural number]]s to a subring of the ring of real numbers. Then, a [[natural number]] <math>n</math> is termed a '''minimum-so-far''' for <math>f</math> if <math>f(n) < f(m)</math> for all natural numbers <math>m < n</math>.<br />
<br />
==Related notions==<br />
<br />
* [[Minimum-so-far]] is a natural number <math>n</math> such that <math>f(n) \le f(m)</math> for <math>m \le n</math>.<br />
* [[Maximum-so-far]] is a natural number <math>n</math> such that <math>f(m) \le f(n)</math> for all <math>m \le n</math>.<br />
* [[Strict maximum-so-far]] is natural number <math>n</math> such that <math>f(m) < f(n)</math> for all <math>m < n</math>.</div>Vipul