https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Elementary_arithmetic 2026-04-17T06:38:31Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&diff=238934&oldid=prev 2014-11-18T19:54:13Z

<p>Not sure if tools need to be discussed in this article, but if they do, it shouldn&#039;t be in the lede.</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 21:54, 18 November 2014</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" 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><del style="font-weight: bold; text-decoration: none;">The author is called Ashlyn Book but she never </del>really <del style="font-weight: bold; text-decoration: none;">liked that name</del>. <del style="font-weight: bold; text-decoration: none;">In my professional life </del>I am <del style="font-weight: bold; text-decoration: none;">an office clerk but soon she and Let me start some of our business</del>. <del style="font-weight: bold; text-decoration: none;">Arkansas </del>is <del style="font-weight: bold; text-decoration: none;">where he and also his wife live </del>but <del style="font-weight: bold; text-decoration: none;">he</del>'<del style="font-weight: bold; text-decoration: none;">ll have to advance one day or 1 more</del>. <del style="font-weight: bold; text-decoration: none;">To collect kites </del>is <del style="font-weight: bold; text-decoration: none;">issue he loves most associated with. If you for you to find out more away </del>my <del style="font-weight: bold; text-decoration: none;">website: http://tinyurl</del>.<del style="font-weight: bold; text-decoration: none;">com/fayereagan67762</del>&lt;br&gt;&lt;br&gt;<del style="font-weight: bold; text-decoration: none;">Visit </del>my <del style="font-weight: bold; text-decoration: none;">website</del>; <del style="font-weight: bold; text-decoration: none;">faye reagan videos, </del>[http://<del style="font-weight: bold; text-decoration: none;">tinyurl</del>.<del style="font-weight: bold; text-decoration: none;">com/fayereagan67762 http://tinyurl</del>.com/<del style="font-weight: bold; text-decoration: none;">fayereagan67762</del>]<del style="font-weight: bold; text-decoration: none;">,</del></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><ins style="font-weight: bold; text-decoration: none;">Greetings! I am Marvella and I </ins>really <ins style="font-weight: bold; text-decoration: none;">feel comfortable when individuals use the complete title</ins>. I am <ins style="font-weight: bold; text-decoration: none;">a meter reader</ins>. <ins style="font-weight: bold; text-decoration: none;">What I love doing </ins>is <ins style="font-weight: bold; text-decoration: none;">to gather badges </ins>but <ins style="font-weight: bold; text-decoration: none;">I</ins>'<ins style="font-weight: bold; text-decoration: none;">ve been taking on new issues lately</ins>. <ins style="font-weight: bold; text-decoration: none;">North Dakota </ins>is <ins style="font-weight: bold; text-decoration: none;">where me and </ins>my <ins style="font-weight: bold; text-decoration: none;">spouse reside</ins>.&lt;br&gt;&lt;br&gt;<ins style="font-weight: bold; text-decoration: none;">Here is </ins>my <ins style="font-weight: bold; text-decoration: none;">web-site</ins>; [http://<ins style="font-weight: bold; text-decoration: none;">Tomjones1190</ins>.<ins style="font-weight: bold; text-decoration: none;">livejournal</ins>.com/ <ins style="font-weight: bold; text-decoration: none;">healthy meals delivered</ins>]</div></td></tr> </table>

en>SebastianHelm https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&diff=238933&oldid=prev 2014-02-12T03:06:24Z

<p><span class="autocomment">Subtraction: </span> added technical terms up front</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 05:06, 12 February 2014</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" 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><del style="font-weight: bold; text-decoration: none;">{{unreferenced|date=August 2007}}</del></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><ins style="font-weight: bold; text-decoration: none;">The author is called Ashlyn Book but she never really liked that name. </ins>In <ins style="font-weight: bold; text-decoration: none;">my professional life I am an office clerk but soon she and Let me start some of our business. Arkansas is where he and also his wife live but he</ins>'<ins style="font-weight: bold; text-decoration: none;">ll have to advance one day or </ins>1 <ins style="font-weight: bold; text-decoration: none;">more. To collect kites </ins>is <ins style="font-weight: bold; text-decoration: none;">issue he loves most associated with</ins>. <ins style="font-weight: bold; text-decoration: none;">If you for you to find out more away my website: http</ins>://<ins style="font-weight: bold; text-decoration: none;">tinyurl</ins>.<ins style="font-weight: bold; text-decoration: none;">com/fayereagan67762</ins>&lt;<ins style="font-weight: bold; text-decoration: none;">br</ins>&gt;&lt;<ins style="font-weight: bold; text-decoration: none;">br</ins>&gt;<ins style="font-weight: bold; text-decoration: none;">Visit my website</ins>; <ins style="font-weight: bold; text-decoration: none;">faye reagan videos</ins>, [<ins style="font-weight: bold; text-decoration: none;">http://tinyurl</ins>.<ins style="font-weight: bold; text-decoration: none;">com/fayereagan67762 http://tinyurl</ins>.<ins style="font-weight: bold; text-decoration: none;">com/fayereagan67762</ins>],</div></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>In <del style="font-weight: bold; text-decoration: none;">[[mathematics]], a </del>'<del style="font-weight: bold; text-decoration: none;">''half-integer''' is a [[number]] of the form </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">:&lt;math&gt;n + {</del>1<del style="font-weight: bold; text-decoration: none;">\over 2}&lt;/math&gt;, </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">where &lt;math&gt;n&lt;/math&gt; </del>is <del style="font-weight: bold; text-decoration: none;">an [[integer]]</del>. <del style="font-weight: bold; text-decoration: none;"> For example, </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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>:<del style="font-weight: bold; text-decoration: none;">4&amp;frac12;, 7</del>/<del style="font-weight: bold; text-decoration: none;">2, &amp;minus;13</del>/<del style="font-weight: bold; text-decoration: none;">2, 8</del>.<del style="font-weight: bold; text-decoration: none;">5</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">are all half-integers. Note that a half of an integer is not always a half-integer: half of an [[even integer]] is an integer but not a half-integer. The half-integers are precisely those numbers that are half of an [[odd integer]].</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">The [[Set (mathematics)|set]] of all half-integers is often denoted </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">:</del>&lt;<del style="font-weight: bold; text-decoration: none;">math</del>&gt;<del style="font-weight: bold; text-decoration: none;">\mathbb Z + {1\over 2}.</del>&lt;<del style="font-weight: bold; text-decoration: none;">/math</del>&gt;</div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">==Uses==</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">Half-integers occur frequently enough in mathematical contexts that a special term for them is convenient. For example, the densest [[lattice packing]] of unit [[sphere]]s in four dimensions places a sphere at every point whose coordinates are either all integers or all half-integers</del>; <del style="font-weight: bold; text-decoration: none;">this packing is closely related to the [[Hurwitz integer]]s</del>, <del style="font-weight: bold; text-decoration: none;">which are </del>[<del style="font-weight: bold; text-decoration: none;">[quaternion]]s whose real coefficients are either all integers or all half-integers</del>. <del style="font-weight: bold; text-decoration: none;"> </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">Moreover, the [[Pauli exclusion principle]] results from definition of [[fermion]]s as particles which have [[spin (physics)|spin]]s that are half-integers</del>. <del style="font-weight: bold; text-decoration: none;">The [[energy level]</del>]<del style="font-weight: bold; text-decoration: none;">s of the [[quantum harmonic oscillator]] occur at half-integers and thus its lowest energy is not zero.</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">Also</del>, <del style="font-weight: bold; text-decoration: none;">the [[factorial]] and [[gamma function]]s, while not defined for [[negative number|negative and non-positive integers]] respectively, are defined for all half-integers as rational multiples of the [[square root]] of [[pi]].</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">[[Category:Rational numbers]]</del></div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">[[Category:Elementary number theory]]</del></div></td><td colspan="2" class="diff-side-added"></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><del style="font-weight: bold; text-decoration: none;">[[Category:Parity]]</del></div></td><td colspan="2" class="diff-side-added"></td></tr> </table>

en>Dhtwiki https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&diff=8822&oldid=prev 2013-11-07T21:34:25Z

<p><span class="autocomment">Subtraction: </span>Typo fixing, replaced: from country from country → from country to country using <a href="/index.php?title=Testwiki:AWB&amp;action=edit&amp;redlink=1" class="new" title="Testwiki:AWB (page does not exist)">AWB</a></p> <a href="https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&amp;diff=8822&amp;oldid=238932">Show changes</a>

en>John of Reading https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&diff=238932&oldid=prev 2012-08-08T02:35:29Z

<p>Undid revision 505993589 by <a href="/wiki/Special:Contributions/203.46.125.249" title="Special:Contributions/203.46.125.249">203.46.125.249</a> (<a href="/index.php?title=User_talk:203.46.125.249&amp;action=edit&amp;redlink=1" class="new" title="User talk:203.46.125.249 (page does not exist)">talk</a>) Why change the numbers?</p> <a href="https://en.formulasearchengine.com/index.php?title=Elementary_arithmetic&amp;diff=238932">Show changes</a>

en>David1217