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Almost all - Revision history
2024-03-29T13:28:05Z
Revision history for this page on the wiki
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https://en.formulasearchengine.com/index.php?title=Almost_all&diff=218551&oldid=prev
en>Brirush at 13:16, 22 November 2014
2014-11-22T13:16:57Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:16, 22 November 2014</td>
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<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;">{{Refimprove|date=January 2010}}</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;">Ed is what individuals call me and my wife doesn</ins>'<ins style="font-weight: bold; text-decoration: none;">t like it at </ins>all<ins style="font-weight: bold; text-decoration: none;">. I</ins>'<ins style="font-weight: bold; text-decoration: none;">ve usually loved living in Kentucky but now I</ins>'<ins style="font-weight: bold; text-decoration: none;">m contemplating other choices</ins>. <ins style="font-weight: bold; text-decoration: none;">To climb </ins>is <ins style="font-weight: bold; text-decoration: none;">something I really enjoy doing</ins>. <ins style="font-weight: bold; text-decoration: none;">Distributing manufacturing </ins>is <ins style="font-weight: bold; text-decoration: none;">how he makes </ins>a <ins style="font-weight: bold; text-decoration: none;">living</ins>.<ins style="font-weight: bold; text-decoration: none;"><br><br>Also visit my weblog :</ins>: <ins style="font-weight: bold; text-decoration: none;">free psychic readings </ins>([<ins style="font-weight: bold; text-decoration: none;">http</ins>://<ins style="font-weight: bold; text-decoration: none;">www.christmaslightshowvideos</ins>.<ins style="font-weight: bold; text-decoration: none;">com</ins>/<ins style="font-weight: bold; text-decoration: none;">profile</ins>.<ins style="font-weight: bold; text-decoration: none;">php?u=MiNrr click here! www</ins>.<ins style="font-weight: bold; text-decoration: none;">christmaslightshowvideos</ins>.<ins style="font-weight: bold; text-decoration: none;">com</ins>]<ins style="font-weight: bold; text-decoration: none;">)</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><del style="font-weight: bold; text-decoration: none;">In [[mathematics]], the phrase </del>'<del style="font-weight: bold; text-decoration: none;">''"almost </del>all<del style="font-weight: bold; text-decoration: none;">"</del>''<del style="font-weight: bold; text-decoration: none;">' has a number of specialised 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;">"Almost all" is sometimes used synonymously with "all but [except] [[finite set|finite]]ly many" (formally, a [[cofinite]] set) or "all but a [[countable set]]" (formally, a [[cocountable]] set); see [[almost]]</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;">A simple example </del>is <del style="font-weight: bold; text-decoration: none;">that almost all prime numbers are odd, which is based on the fact that all but one prime number is odd</del>. <del style="font-weight: bold; text-decoration: none;"> (The exception </del>is <del style="font-weight: bold; text-decoration: none;">the number 2, which is prime but not odd.)</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;">When speaking about the [[real number|reals]], sometimes it means "all reals but </del>a <del style="font-weight: bold; text-decoration: none;">set of [[Lebesgue measure]] zero" (formally, [[almost everywhere]])</del>. <del style="font-weight: bold; text-decoration: none;">In this sense almost all reals are not a member of the [[Cantor set]] even though the Cantor set is [[Uncountable set|uncountable]].</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;">In [[number theory]], if ''P''(''n'') is a property of positive [[integer]]s, and if ''p''(''N'') denotes the number of [[positive integers]] ''n'' less than ''N'' for which ''P''(''n'') holds, and if </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;">''p''(''N'')/''N'' → 1 as ''N'' → ∞</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;">(see [[Limit of a sequence|limit]]), then we say that "''P''(''n'') holds for almost all positive integers ''n''" </del>(<del style="font-weight: bold; text-decoration: none;">formally, </del>[<del style="font-weight: bold; text-decoration: none;">[asymptotically almost surely]]) and write</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;"><math>(\forall^\infty n) P(n).<</del>/<del style="font-weight: bold; text-decoration: none;">math></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;">For example, the [[prime number theorem]] states that the number of [[prime numbers]] less than or equal to ''N'' is asymptotically equal to ''N''</del>/<del style="font-weight: bold; text-decoration: none;">ln ''N''</del>. <del style="font-weight: bold; text-decoration: none;">Therefore the proportion of prime integers is roughly 1</del>/<del style="font-weight: bold; text-decoration: none;">ln ''N'', which tends to 0</del>. <del style="font-weight: bold; text-decoration: none;">Thus, ''almost all'' positive integers are [[composite number|composite]] (not prime), however there are still an infinite number of primes</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;">Occasionally, "almost all" is used in the sense of "[[almost everywhere]]" in [[measure theory]], or in the closely related sense of "[[almost surely]]" in [[probability 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> </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;">==See also==</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;">*[[Generic property]]</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;">*[[Sufficiently large]]</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;">==References==</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;">*{{MathWorld|title=Almost All|urlname=AlmostAll}}</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;">{{DEFAULTSORT:Almost All}}</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:Mathematical terminology]]</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:Mathematical notation]</del>]</div></td><td colspan="2" class="diff-side-added"></td></tr>
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en>Brirush
https://en.formulasearchengine.com/index.php?title=Almost_all&diff=28&oldid=prev
en>Omnipaedista: per WP:APPENDIX
2013-11-17T09:31:39Z
<p>per <a href="/index.php?title=WP:APPENDIX&action=edit&redlink=1" class="new" title="WP:APPENDIX (page does not exist)">WP:APPENDIX</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:31, 17 November 2013</td>
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<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 calorie calculator is </del>a <del style="font-weight: bold; text-decoration: none;">easy fat loss tool</del>. <del style="font-weight: bold; text-decoration: none;">This calculator </del>is <del style="font-weight: bold; text-decoration: none;">built because </del>a <del style="font-weight: bold; text-decoration: none;">software package which will allow we to list each meal daily. It might select </del>all <del style="font-weight: bold; text-decoration: none;">foods you consumed and calculate the calories per item and amount consumed. After gathering the information it usually then total the calories per meal. Every day you do this it usually offer you with </del>a <del style="font-weight: bold; text-decoration: none;">total daily caloric intake report</del>. <del style="font-weight: bold; text-decoration: none;"> The calorie calculator </del>is <del style="font-weight: bold; text-decoration: none;">not an actual instrument however</del>, <del style="font-weight: bold; text-decoration: none;">extremely close. It offers estimates but usually point you inside the appropriate direction to what we require to do to lose fat.<br><br>After this, you are able to move </del>on <del style="font-weight: bold; text-decoration: none;">to calculate </del>the <del style="font-weight: bold; text-decoration: none;">Body Mass Index (BMI). Input height plus weight for your BMI and how this classifies we. I came out because obese, </del>that is <del style="font-weight: bold; text-decoration: none;">understandable, as I nonetheless have about calorie burn calculator 15 - 20lbs to lose</del>. <del style="font-weight: bold; text-decoration: none;">You can also be presented with </del>the <del style="font-weight: bold; text-decoration: none;">perfect BMI range. There's moreover a Lean Body Mass calculator, that estimates the fat of muscles, organs, blood plus water inside the body.<br><br>I plugged inside my present stats, plus if I wish to lose 100 pounds in 1 year, I want to eat 1261 calories a day. If I like to lose 100 pounds inside </del>2 <del style="font-weight: bold; text-decoration: none;">years</del>, <del style="font-weight: bold; text-decoration: none;">I can eat 1716 calories a day. You can follow my fat reduction journey by visiting my weight loss.<br><br>Walking up plus down the stairs </del>is <del style="font-weight: bold; text-decoration: none;">a superior exercise to burn calories</del>. <del style="font-weight: bold; text-decoration: none;">Approximately 300 calories is burned by strolling </del>the <del style="font-weight: bold; text-decoration: none;">stairs for regarding 30 minutes. Doesn't which sound like a considerable big </del>[<del style="font-weight: bold; text-decoration: none;">http://safedietplansforwomen.com/calories-burned-walking calories burned walking</del>] <del style="font-weight: bold; text-decoration: none;">amount? But</del>, it <del style="font-weight: bold; text-decoration: none;">definitely is </del>a <del style="font-weight: bold; text-decoration: none;">lot </del>of <del style="font-weight: bold; text-decoration: none;">difficult work</del>.<del style="font-weight: bold; text-decoration: none;"><br><br>Thirdly, it </del>all <del style="font-weight: bold; text-decoration: none;">comes right down to might force. Do </del>not <del style="font-weight: bold; text-decoration: none;">allow yourself to overeat. No matter how strong </del>the <del style="font-weight: bold; text-decoration: none;">desire to receive another calories burned calculator serving could be, do your ideal to overcome </del>the <del style="font-weight: bold; text-decoration: none;">temptation</del>. <del style="font-weight: bold; text-decoration: none;">You </del>is <del style="font-weight: bold; text-decoration: none;">grateful we did!<br><br>Considering this</del>, the <del style="font-weight: bold; text-decoration: none;">solution seems clear: receive yourself outside </del>for <del style="font-weight: bold; text-decoration: none;">a 30-minute run six instances a week</del>, and <del style="font-weight: bold; text-decoration: none;">youll burn an additional 3200 calories </del>a <del style="font-weight: bold; text-decoration: none;">week. If you keep a diet the same</del>, <del style="font-weight: bold; text-decoration: none;">which means youll be losing about a pound every week </del>(<del style="font-weight: bold; text-decoration: none;">to lose one pound you should burn 3500 more calories than you take in</del>)<del style="font-weight: bold; text-decoration: none;">. Needless to say</del>, <del style="font-weight: bold; text-decoration: none;">just starting a running program is easier said than performed. If you are obese or from shape, even running a mile will feel impossible.</del><<del style="font-weight: bold; text-decoration: none;">br</del>><<del style="font-weight: bold; text-decoration: none;">br</del>><del style="font-weight: bold; text-decoration: none;">The key </del>to <del style="font-weight: bold; text-decoration: none;">not falling prey </del>to <del style="font-weight: bold; text-decoration: none;">such supermarket schemes </del>is '<del style="font-weight: bold; text-decoration: none;">mind control</del>'. <del style="font-weight: bold; text-decoration: none;">It</del>'<del style="font-weight: bold; text-decoration: none;">s </del>all <del style="font-weight: bold; text-decoration: none;">in the mind! Keep telling yourself you</del>'<del style="font-weight: bold; text-decoration: none;">re </del>not <del style="font-weight: bold; text-decoration: none;">going to succumb to any temptation</del>. <del style="font-weight: bold; text-decoration: none;">If you win </del>the <del style="font-weight: bold; text-decoration: none;">battle </del>in <del style="font-weight: bold; text-decoration: none;">the notice</del>, <del style="font-weight: bold; text-decoration: none;">you may be sure to have self control </del>in the <del style="font-weight: bold; text-decoration: none;">mall. Being certain about what we want, will aid avoid indulging </del>in <del style="font-weight: bold; text-decoration: none;">impulse obtaining</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;">{{Refimprove|date=January 2010}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">In [[mathematics]], the phrase '''"almost all"''' has </ins>a <ins style="font-weight: bold; text-decoration: none;">number of specialised uses</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">"Almost all" </ins>is <ins style="font-weight: bold; text-decoration: none;">sometimes used synonymously with "all but [except] [[finite set|finite]]ly many" (formally, </ins>a <ins style="font-weight: bold; text-decoration: none;">[[cofinite]] set) or "</ins>all <ins style="font-weight: bold; text-decoration: none;">but a [[countable set]]" (formally, </ins>a <ins style="font-weight: bold; text-decoration: none;">[[cocountable]] set); see [[almost]]</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">A simple example </ins>is <ins style="font-weight: bold; text-decoration: none;">that almost all prime numbers are odd</ins>, <ins style="font-weight: bold; text-decoration: none;">which is based </ins>on the <ins style="font-weight: bold; text-decoration: none;">fact </ins>that <ins style="font-weight: bold; text-decoration: none;">all but one prime number </ins>is <ins style="font-weight: bold; text-decoration: none;">odd</ins>. <ins style="font-weight: bold; text-decoration: none;"> (The exception is </ins>the <ins style="font-weight: bold; text-decoration: none;">number </ins>2, <ins style="font-weight: bold; text-decoration: none;">which </ins>is <ins style="font-weight: bold; text-decoration: none;">prime but not odd</ins>.<ins style="font-weight: bold; text-decoration: none;">)</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">When speaking about </ins>the [<ins style="font-weight: bold; text-decoration: none;">[real number|reals]</ins>], <ins style="font-weight: bold; text-decoration: none;">sometimes </ins>it <ins style="font-weight: bold; text-decoration: none;">means "all reals but </ins>a <ins style="font-weight: bold; text-decoration: none;">set </ins>of <ins style="font-weight: bold; text-decoration: none;">[[Lebesgue measure]] zero" (formally, [[almost everywhere]])</ins>. <ins style="font-weight: bold; text-decoration: none;">In this sense almost </ins>all <ins style="font-weight: bold; text-decoration: none;">reals are </ins>not <ins style="font-weight: bold; text-decoration: none;">a member of </ins>the <ins style="font-weight: bold; text-decoration: none;">[[Cantor set]] even though </ins>the <ins style="font-weight: bold; text-decoration: none;">Cantor set is [[Uncountable set|uncountable]]</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">In [[number theory]], if ''P''(''n'') </ins>is <ins style="font-weight: bold; text-decoration: none;">a property of positive [[integer]]s</ins>, <ins style="font-weight: bold; text-decoration: none;">and if ''p''(''N'') denotes </ins>the <ins style="font-weight: bold; text-decoration: none;">number of [[positive integers]] ''n'' less than ''N'' </ins>for <ins style="font-weight: bold; text-decoration: none;">which ''P''(''n'') holds</ins>, and <ins style="font-weight: bold; text-decoration: none;">if </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">:''p''(''N'')/''N'' → 1 as ''N'' → ∞</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">(see [[Limit of </ins>a <ins style="font-weight: bold; text-decoration: none;">sequence|limit]])</ins>, <ins style="font-weight: bold; text-decoration: none;">then we say that "''P''</ins>(<ins style="font-weight: bold; text-decoration: none;">''n''</ins>) <ins style="font-weight: bold; text-decoration: none;">holds for almost all positive integers ''n''" (formally</ins>, <ins style="font-weight: bold; text-decoration: none;">[[asymptotically almost surely]]) and write</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">:</ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">(\forall^\infty n) P(n).</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">For example, the [[prime number theorem]] states that the number of [[prime numbers]] less than or equal </ins>to <ins style="font-weight: bold; text-decoration: none;">''N'' is asymptotically equal </ins>to <ins style="font-weight: bold; text-decoration: none;">''N''/ln ''N''. Therefore the proportion of prime integers </ins>is <ins style="font-weight: bold; text-decoration: none;">roughly 1/ln ''N</ins>''<ins style="font-weight: bold; text-decoration: none;">, which tends to 0</ins>. <ins style="font-weight: bold; text-decoration: none;">Thus, '</ins>'<ins style="font-weight: bold; text-decoration: none;">almost </ins>all'<ins style="font-weight: bold; text-decoration: none;">' positive integers are [[composite number|composite]] (</ins>not <ins style="font-weight: bold; text-decoration: none;">prime), however there are still an infinite number of primes</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">Occasionally, "almost all" is used in </ins>the <ins style="font-weight: bold; text-decoration: none;">sense of "[[almost everywhere]]" </ins>in <ins style="font-weight: bold; text-decoration: none;">[[measure theory]]</ins>, <ins style="font-weight: bold; text-decoration: none;">or </ins>in the <ins style="font-weight: bold; text-decoration: none;">closely related sense of "[[almost surely]]" </ins>in <ins style="font-weight: bold; text-decoration: none;">[[probability theory]]</ins>.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">==See also==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">*[[Generic property]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">*[[Sufficiently large]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">==References==</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">*{{MathWorld|title=Almost All|urlname=AlmostAll}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">{{DEFAULTSORT:Almost All}}</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">[[Category:Mathematical terminology]]</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></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;">[[Category:Mathematical notation]]</ins></div></td></tr>
</table>
en>Omnipaedista
https://en.formulasearchengine.com/index.php?title=Almost_all&diff=218550&oldid=prev
en>Johnfloyd6675 at 12:29, 20 May 2012
2012-05-20T12:29:46Z
<p></p>
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en>Johnfloyd6675