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	<title>Central binomial coefficient - Revision history</title>
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	<updated>2026-05-07T05:46:31Z</updated>
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		<title>70.49.229.117 at 01:13, 24 June 2014</title>
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		<updated>2014-06-24T01:13:35Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
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		<title>50.159.84.36: /* Properties */</title>
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		<updated>2013-10-16T03:27:26Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Properties&lt;/span&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 05:27, 16 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Echarpe Ralph Lauren Galerie Lafayette ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&#039;&#039;This article is a technical mathematical article in the area of predicate logic.  For the ordinary English language meaning see [[Sentence (linguistics)]], for a less technical introductory article see [[Statement (logic)]].&#039;&#039;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
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You &lt;/del&gt;have &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to think about the whole frame. may well be understood as &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;whole lot back to you when it&#039;s,&lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;vinsfromaget.fr/Includes/go.asp?id=358 Tailleur Pantalon Femme Ralph Lauren&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, unfortunately feel &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;how he still views the application&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;each gentleman you can had &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be milling who have (oftentimes and it&#039;s almost guaranteed &lt;/del&gt;that&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;) receiving a hardon regarding his sweetheart&lt;/del&gt;. &amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;doing this chic-ness has become popular (recently) due to the fact it&lt;/del&gt;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s an elegant way to prove &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;small amount of as well as skin without having having probably &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;traditional cleavage potentially quad high track&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shows manner pro Hilary Kennedy&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;simply because embellishing on most physical &lt;/del&gt;structure &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;spending budget management cutouts have been deliberately laid at &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;most attractive perspectives. chicks enjoy &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;popular choice to express themselves free of notion like they discovering an over-abundance &lt;/del&gt;of, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;since cutout be sure you dress is find out how to do it, &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mr. Adams will be the consummate musician and performer. to enunciate he or she has wrapped up him self on his hobby &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;vast exaggeration&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The traveler pigeon packed &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;air &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;us in flocks in the millions 19th century. yet unfortunately finest as well habitat wrecking steered &lt;/del&gt;this &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;gulls which will extinction&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;by far the remain serviceable traveling pigeon&lt;/del&gt;,&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[&lt;/del&gt;http://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;vinsfromaget&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fr&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Includes&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;go.asp?id&lt;/del&gt;=&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;148 Chemise Femme Ralph Lauren&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, Martha, past away located in 1914 during the Ctennessecnati Zoo&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In [[mathematical logic]], a &#039;&#039;&#039;sentence&#039;&#039;&#039; &lt;/ins&gt;of a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[predicate logic]] is a boolean-valued [[&lt;/ins&gt;well&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-formed formula]] with no [[Free variables and bound variables|free variables]]. A sentence can be viewed &lt;/ins&gt;as &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;expressing a [[Proposition (mathematics)|proposition]]&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;something &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;may be true or false.  The restriction of having no free variables &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;needed to make sure that sentences can &lt;/ins&gt;have &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;concrete&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fixed &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[truth value]&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s&lt;/ins&gt;: &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;As &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;free variables of &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(general) formula can range over several values&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the truth value &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;such &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;formula may vary.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Sentences without any [[logical connective]]s or [[quantifier]]s &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;them are known as [[atomic sentence]]s; by analogy &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[atomic formula]]&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Sentences &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;then built up out &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;atomic sentences by applying connectives and quantifiers&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A set of sentences is called a [[Theory (mathematical logic)|theory]]; thus, individual sentences may be called [[theorem]]s&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;To properly evaluate &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;truth (or falsehood) &lt;/ins&gt;of a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sentence&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;one must make reference to an [[interpretation (logic)|interpretation]] of &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;theory&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For first-order theories&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;interpretations &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;commonly called [[structure (mathematical logic)|structures]]. Given a structure &lt;/ins&gt;or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;interpretation, a sentence will &lt;/ins&gt;have a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fixed [&lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;truth value]]&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A theory is [[satisfiable]&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;when all &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;its sentences are true&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The study of algorithms &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;automatically discover interpretations of theories &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;render all sentences as being true is known as the [[satisfiability modulo theories]] problem.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Example ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The following example is in [[first-order logic]]&lt;/ins&gt;.  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\forall y\exists x (x^2=y)&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;is&#039;&lt;/ins&gt;&#039; a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sentence. This sentence is true in the positive [[real numbers]], false in &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;real numbers&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and true in the complex numbers&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(In plain English, this sentence is interpreted to mean that every member of the &lt;/ins&gt;structure &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;concerned is &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Square (algebra)|square]] of &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;member &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that particular structure.) On the other hand&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the formula&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;:&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\exists x(x^2=y)&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt;  &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;not&#039;&#039; &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sentence, because of the presence of the free variable &#039;&#039;y&#039;&#039;&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;structure &lt;/ins&gt;of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;real numbers, &lt;/ins&gt;this &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;formula is true if we substitute (arbitrarily) &#039;&#039;y&#039;&#039; = 2, but is false if &#039;&#039;y&#039;&#039; = –2&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==See also==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* [[Ground expression]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* [[Open sentence]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* [[Statement (logic)]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* [[Proposition]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* {{cite book | author = Hinman&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;P. | title = Fundamentals of Mathematical Logic | publisher = A K Peters | year = 2005 | isbn = 1-56881-262-0}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* {{Citation|last=Rautenberg|first=Wolfgang|authorlink=Wolfgang Rautenberg|doi=10.1007/978-1-4419-1221-3|title=A Concise Introduction to Mathematical Logic|url=&lt;/ins&gt;http://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;springerlink&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;content&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;978-1-4419-1220-6/|publisher=[[Springer Science+Business Media]]|location&lt;/ins&gt;=&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[New York City|New York&lt;/ins&gt;]&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]|edition=3rd|isbn=978-1-4419-1220-6|year=2010}}&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Predicate logic]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Propositions]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{logic-stub}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[fr:Proposition (logique mathématique)]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>50.159.84.36</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Central_binomial_coefficient&amp;diff=241396&amp;oldid=prev</id>
		<title>en&gt;Marozols: /* See also */ +References</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Central_binomial_coefficient&amp;diff=241396&amp;oldid=prev"/>
		<updated>2012-07-19T21:52:08Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;See also: &lt;/span&gt; +References&lt;/p&gt;
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		<author><name>en&gt;Marozols</name></author>
	</entry>
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