https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3AContribution%2FFactor_Limit
User:Contribution/Factor Limit - Revision history
2026-06-23T14:02:04Z
Revision history for this page on the wiki
MediaWiki 1.43.6
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47171&oldid=prev
Contribution: /* Examples */
2020-06-19T12:15:51Z
<p><span class="autocomment">Examples</span></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 12:15, 19 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l62">Line 62:</td>
<td colspan="2" class="diff-lineno">Line 62:</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* ((5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit) × (3;3;0;26)-limit × (2;2;0;+∞)-limit is represented by [[User:Contribution/(31-Limit_Factor_Gradient)_x_(26_Tritaves_Chain)|this table]].</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>* ((5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit) × (3;3;0;26)-limit × (2;2;0;+∞)-limit is represented by [[User:Contribution/(31-Limit_Factor_Gradient)_x_(26_Tritaves_Chain<ins style="font-weight: bold; text-decoration: none;">)_x_(Infinite_Octaves</ins>)|this table]].</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47163&oldid=prev
Contribution: /* Examples */
2020-06-19T12:00:39Z
<p><span class="autocomment">Examples</span></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 12:00, 19 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l62">Line 62:</td>
<td colspan="2" class="diff-lineno">Line 62:</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* ( (5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit ) × <del style="font-weight: bold; text-decoration: none;">( </del>(3;3;0;26)-limit <del style="font-weight: bold; text-decoration: none;">∪ </del>(2;2;0;+∞)-limit <del style="font-weight: bold; text-decoration: none;">) </del>is represented by [[User:Contribution/(31-Limit_Factor_Gradient)_x_(26_Tritaves_Chain)|this table]].</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>* ((5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit) × (3;3;0;26)-limit <ins style="font-weight: bold; text-decoration: none;">× </ins>(2;2;0;+∞)-limit is represented by [[User:Contribution/(31-Limit_Factor_Gradient)_x_(26_Tritaves_Chain)|this table]].</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47043&oldid=prev
Contribution: /* Definition */
2020-06-17T18:50:50Z
<p><span class="autocomment">Definition</span></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 18:50, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l62">Line 62:</td>
<td colspan="2" class="diff-lineno">Line 62:</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* ( (5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit ) × ( (3;3;0;26)-limit ∪ (2;2;0;+∞)-limit ) is represented by this table</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>* ( (5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit ) × ( (3;3;0;26)-limit ∪ (2;2;0;+∞)-limit ) is represented by <ins style="font-weight: bold; text-decoration: none;">[[User:Contribution/(31-Limit_Factor_Gradient)_x_(26_Tritaves_Chain)|</ins>this table<ins style="font-weight: bold; text-decoration: none;">]].</ins></div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47028&oldid=prev
Contribution: /* Examples */
2020-06-17T13:05:47Z
<p><span class="autocomment">Examples</span></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 13:05, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l61">Line 61:</td>
<td colspan="2" class="diff-lineno">Line 61:</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2/1, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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></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;">* ( (5;7;0;3)-limit ∪ (5;13;0;2)-limit ∪ (5;31;0;1)-limit ) × ( (3;3;0;26)-limit ∪ (2;2;0;+∞)-limit ) is represented by this table</ins></div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47027&oldid=prev
Contribution: /* Definition */
2020-06-17T12:46:21Z
<p><span class="autocomment">Definition</span></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 12:46, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l60">Line 60:</td>
<td colspan="2" class="diff-lineno">Line 60:</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>* (3;3;0;26)-limit contains only 1/1, 3/1, 1/3, 3<sup>2</sup>, 3<sup>-2</sup>, 3<sup>3</sup>, 3<sup>-3</sup>, 3<sup>4</sup>, 3<sup>-4</sup>, 3<sup>5</sup>, 3<sup>-5</sup>, 3<sup>6</sup>, 3<sup>-6</sup>, 3<sup>7</sup>, 3<sup>-7</sup>, 3<sup>8</sup>, 3<sup>-8</sup>, 3<sup>9</sup>, 3<sup>-9</sup>, 3<sup>10</sup>, 3<sup>-10</sup>, 3<sup>11</sup>, 3<sup>-11</sup>, 3<sup>12</sup>, 3<sup>-12</sup>, 3<sup>13</sup>, 3<sup>-13</sup>, 3<sup>14</sup>, 3<sup>-14</sup>, 3<sup>15</sup>, 3<sup>-15</sup>, 3<sup>16</sup>, 3<sup>-16</sup>, 3<sup>17</sup>, 3<sup>-17</sup>, 3<sup>18</sup>, 3<sup>-18</sup>, 3<sup>19</sup>, 3<sup>-19</sup>, 3<sup>20</sup>, 3<sup>-20</sup>, 3<sup>21</sup>, 3<sup>-21</sup>, 3<sup>22</sup>, 3<sup>-22</sup>, 3<sup>23</sup>, 3<sup>-23</sup>, 3<sup>24</sup>, 3<sup>-24</sup>, 3<sup>25</sup>, 3<sup>-25</sup>, 3<sup>26</sup>, 3<sup>-26</sup>.</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>* (3;3;0;26)-limit contains only 1/1, 3/1, 1/3, 3<sup>2</sup>, 3<sup>-2</sup>, 3<sup>3</sup>, 3<sup>-3</sup>, 3<sup>4</sup>, 3<sup>-4</sup>, 3<sup>5</sup>, 3<sup>-5</sup>, 3<sup>6</sup>, 3<sup>-6</sup>, 3<sup>7</sup>, 3<sup>-7</sup>, 3<sup>8</sup>, 3<sup>-8</sup>, 3<sup>9</sup>, 3<sup>-9</sup>, 3<sup>10</sup>, 3<sup>-10</sup>, 3<sup>11</sup>, 3<sup>-11</sup>, 3<sup>12</sup>, 3<sup>-12</sup>, 3<sup>13</sup>, 3<sup>-13</sup>, 3<sup>14</sup>, 3<sup>-14</sup>, 3<sup>15</sup>, 3<sup>-15</sup>, 3<sup>16</sup>, 3<sup>-16</sup>, 3<sup>17</sup>, 3<sup>-17</sup>, 3<sup>18</sup>, 3<sup>-18</sup>, 3<sup>19</sup>, 3<sup>-19</sup>, 3<sup>20</sup>, 3<sup>-20</sup>, 3<sup>21</sup>, 3<sup>-21</sup>, 3<sup>22</sup>, 3<sup>-22</sup>, 3<sup>23</sup>, 3<sup>-23</sup>, 3<sup>24</sup>, 3<sup>-24</sup>, 3<sup>25</sup>, 3<sup>-25</sup>, 3<sup>26</sup>, 3<sup>-26</sup>.</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>* (2;2;0;+∞)-limit contains only 1/1, 2, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2<ins style="font-weight: bold; text-decoration: none;">/1</ins>, 1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47026&oldid=prev
Contribution: /* Examples */
2020-06-17T12:46:10Z
<p><span class="autocomment">Examples</span></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 12:46, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l60">Line 60:</td>
<td colspan="2" class="diff-lineno">Line 60:</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>* (3;3;0;26)-limit contains only 1/1, 3/1, 1/3, 3<sup>2</sup>, 3<sup>-2</sup>, 3<sup>3</sup>, 3<sup>-3</sup>, 3<sup>4</sup>, 3<sup>-4</sup>, 3<sup>5</sup>, 3<sup>-5</sup>, 3<sup>6</sup>, 3<sup>-6</sup>, 3<sup>7</sup>, 3<sup>-7</sup>, 3<sup>8</sup>, 3<sup>-8</sup>, 3<sup>9</sup>, 3<sup>-9</sup>, 3<sup>10</sup>, 3<sup>-10</sup>, 3<sup>11</sup>, 3<sup>-11</sup>, 3<sup>12</sup>, 3<sup>-12</sup>, 3<sup>13</sup>, 3<sup>-13</sup>, 3<sup>14</sup>, 3<sup>-14</sup>, 3<sup>15</sup>, 3<sup>-15</sup>, 3<sup>16</sup>, 3<sup>-16</sup>, 3<sup>17</sup>, 3<sup>-17</sup>, 3<sup>18</sup>, 3<sup>-18</sup>, 3<sup>19</sup>, 3<sup>-19</sup>, 3<sup>20</sup>, 3<sup>-20</sup>, 3<sup>21</sup>, 3<sup>-21</sup>, 3<sup>22</sup>, 3<sup>-22</sup>, 3<sup>23</sup>, 3<sup>-23</sup>, 3<sup>24</sup>, 3<sup>-24</sup>, 3<sup>25</sup>, 3<sup>-25</sup>, 3<sup>26</sup>, 3<sup>-26</sup>.</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>* (3;3;0;26)-limit contains only 1/1, 3/1, 1/3, 3<sup>2</sup>, 3<sup>-2</sup>, 3<sup>3</sup>, 3<sup>-3</sup>, 3<sup>4</sup>, 3<sup>-4</sup>, 3<sup>5</sup>, 3<sup>-5</sup>, 3<sup>6</sup>, 3<sup>-6</sup>, 3<sup>7</sup>, 3<sup>-7</sup>, 3<sup>8</sup>, 3<sup>-8</sup>, 3<sup>9</sup>, 3<sup>-9</sup>, 3<sup>10</sup>, 3<sup>-10</sup>, 3<sup>11</sup>, 3<sup>-11</sup>, 3<sup>12</sup>, 3<sup>-12</sup>, 3<sup>13</sup>, 3<sup>-13</sup>, 3<sup>14</sup>, 3<sup>-14</sup>, 3<sup>15</sup>, 3<sup>-15</sup>, 3<sup>16</sup>, 3<sup>-16</sup>, 3<sup>17</sup>, 3<sup>-17</sup>, 3<sup>18</sup>, 3<sup>-18</sup>, 3<sup>19</sup>, 3<sup>-19</sup>, 3<sup>20</sup>, 3<sup>-20</sup>, 3<sup>21</sup>, 3<sup>-21</sup>, 3<sup>22</sup>, 3<sup>-22</sup>, 3<sup>23</sup>, 3<sup>-23</sup>, 3<sup>24</sup>, 3<sup>-24</sup>, 3<sup>25</sup>, 3<sup>-25</sup>, 3<sup>26</sup>, 3<sup>-26</sup>.</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>* (2;2;0;+∞)-limit contains only 1/1, 2<del style="font-weight: bold; text-decoration: none;"><sup></del>1<del style="font-weight: bold; text-decoration: none;"><</del>/<del style="font-weight: bold; text-decoration: none;">sup>, </del>2<del style="font-weight: bold; text-decoration: none;"><sup>-1</sup></del>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2<ins style="font-weight: bold; text-decoration: none;">, </ins>1/2, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47025&oldid=prev
Contribution: /* Definition */
2020-06-17T12:45:46Z
<p><span class="autocomment">Definition</span></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 12:45, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l58">Line 58:</td>
<td colspan="2" class="diff-lineno">Line 58:</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>* (5;31;0;1)-limit contains only 1/1, 5/1, 1/5, 7/1, 1/7, 11/1, 1/11, 13/1, 1/13, 17/1, 1/17, 19/1, 1/19, 23/1, 1/23, 29/1, 1/29, 31/1, 1/31.</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>* (5;31;0;1)-limit contains only 1/1, 5/1, 1/5, 7/1, 1/7, 11/1, 1/11, 13/1, 1/13, 17/1, 1/17, 19/1, 1/19, 23/1, 1/23, 29/1, 1/29, 31/1, 1/31.</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>* (3;3;0;26)-limit contains only 3<del style="font-weight: bold; text-decoration: none;"><sup>-26<</del>/<del style="font-weight: bold; text-decoration: none;">sup></del>, 3<del style="font-weight: bold; text-decoration: none;"><sup>-25</sup></del>, 3<sup><del style="font-weight: bold; text-decoration: none;">-24</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">23</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-22</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">21</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-20</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">19</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-18</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">17</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-16</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">15</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-14</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">13</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-12</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">11</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-10</del></sup>, 3<sup>-9</sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-8</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">7</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-6</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">5</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-4</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">3</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">-2</del></sup>, 3<sup>-<del style="font-weight: bold; text-decoration: none;">1</del></sup><del style="font-weight: bold; text-decoration: none;">, 1/1</del>, 3<sup><del style="font-weight: bold; text-decoration: none;">1</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">2</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">3</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">4</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">5</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">6</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">7</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">8</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">9</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">10</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">11</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">12</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">13</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">14</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">15</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">16</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">17</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">18</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">19</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">20</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">21</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">22</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">23</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">24</del></sup>, 3<sup><del style="font-weight: bold; text-decoration: none;">25</del></sup>, 3<sup>26</sup>.</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>* (3;3;0;26)-limit contains only <ins style="font-weight: bold; text-decoration: none;">1/1, </ins>3/<ins style="font-weight: bold; text-decoration: none;">1</ins>, <ins style="font-weight: bold; text-decoration: none;">1/</ins>3, 3<sup><ins style="font-weight: bold; text-decoration: none;">2</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">2</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">3</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">3</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">4</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">4</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">5</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">5</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">6</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">6</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">7</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">7</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">8</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">8</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">9</ins></sup>, 3<sup>-9</sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">10</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">10</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">11</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">11</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">12</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">12</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">13</ins></sup>, 3<sup>-<ins style="font-weight: bold; text-decoration: none;">13</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">14</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-14</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">15</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-15</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">16</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-16</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">17</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-17</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">18</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-18</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">19</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-19</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">20</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-20</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">21</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-21</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">22</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-22</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">23</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-23</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">24</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-24</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">25</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-25</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">26</ins></sup>, 3<sup><ins style="font-weight: bold; text-decoration: none;">-</ins>26</sup>.</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>* (2;2;0;+∞)-limit contains only 1/1, 2<sup>1</sup>, 2<sup>-1</sup>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only 1/1, 2<sup>1</sup>, 2<sup>-1</sup>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47024&oldid=prev
Contribution: /* Prime-bounded and factor-bounded limit */
2020-06-17T12:43:59Z
<p><span class="autocomment">Prime-bounded and factor-bounded limit</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<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 12:43, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l60">Line 60:</td>
<td colspan="2" class="diff-lineno">Line 60:</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>* (3;3;0;26)-limit contains only 3<sup>-26</sup>, 3<sup>-25</sup>, 3<sup>-24</sup>, 3<sup>-23</sup>, 3<sup>-22</sup>, 3<sup>-21</sup>, 3<sup>-20</sup>, 3<sup>-19</sup>, 3<sup>-18</sup>, 3<sup>-17</sup>, 3<sup>-16</sup>, 3<sup>-15</sup>, 3<sup>-14</sup>, 3<sup>-13</sup>, 3<sup>-12</sup>, 3<sup>-11</sup>, 3<sup>-10</sup>, 3<sup>-9</sup>, 3<sup>-8</sup>, 3<sup>-7</sup>, 3<sup>-6</sup>, 3<sup>-5</sup>, 3<sup>-4</sup>, 3<sup>-3</sup>, 3<sup>-2</sup>, 3<sup>-1</sup>, 1/1, 3<sup>1</sup>, 3<sup>2</sup>, 3<sup>3</sup>, 3<sup>4</sup>, 3<sup>5</sup>, 3<sup>6</sup>, 3<sup>7</sup>, 3<sup>8</sup>, 3<sup>9</sup>, 3<sup>10</sup>, 3<sup>11</sup>, 3<sup>12</sup>, 3<sup>13</sup>, 3<sup>14</sup>, 3<sup>15</sup>, 3<sup>16</sup>, 3<sup>17</sup>, 3<sup>18</sup>, 3<sup>19</sup>, 3<sup>20</sup>, 3<sup>21</sup>, 3<sup>22</sup>, 3<sup>23</sup>, 3<sup>24</sup>, 3<sup>25</sup>, 3<sup>26</sup>.</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>* (3;3;0;26)-limit contains only 3<sup>-26</sup>, 3<sup>-25</sup>, 3<sup>-24</sup>, 3<sup>-23</sup>, 3<sup>-22</sup>, 3<sup>-21</sup>, 3<sup>-20</sup>, 3<sup>-19</sup>, 3<sup>-18</sup>, 3<sup>-17</sup>, 3<sup>-16</sup>, 3<sup>-15</sup>, 3<sup>-14</sup>, 3<sup>-13</sup>, 3<sup>-12</sup>, 3<sup>-11</sup>, 3<sup>-10</sup>, 3<sup>-9</sup>, 3<sup>-8</sup>, 3<sup>-7</sup>, 3<sup>-6</sup>, 3<sup>-5</sup>, 3<sup>-4</sup>, 3<sup>-3</sup>, 3<sup>-2</sup>, 3<sup>-1</sup>, 1/1, 3<sup>1</sup>, 3<sup>2</sup>, 3<sup>3</sup>, 3<sup>4</sup>, 3<sup>5</sup>, 3<sup>6</sup>, 3<sup>7</sup>, 3<sup>8</sup>, 3<sup>9</sup>, 3<sup>10</sup>, 3<sup>11</sup>, 3<sup>12</sup>, 3<sup>13</sup>, 3<sup>14</sup>, 3<sup>15</sup>, 3<sup>16</sup>, 3<sup>17</sup>, 3<sup>18</sup>, 3<sup>19</sup>, 3<sup>20</sup>, 3<sup>21</sup>, 3<sup>22</sup>, 3<sup>23</sup>, 3<sup>24</sup>, 3<sup>25</sup>, 3<sup>26</sup>.</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>* (2;2;0;+∞)-limit contains only <del style="font-weight: bold; text-decoration: none;">2<sup>0<</del>/<del style="font-weight: bold; text-decoration: none;">sup></del>, 2<sup>1</sup>, 2<sup>-1</sup>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</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>* (2;2;0;+∞)-limit contains only <ins style="font-weight: bold; text-decoration: none;">1</ins>/<ins style="font-weight: bold; text-decoration: none;">1</ins>, 2<sup>1</sup>, 2<sup>-1</sup>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</div></td></tr>
</table>
Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47023&oldid=prev
Contribution at 12:29, 17 June 2020
2020-06-17T12:29:03Z
<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 12:29, 17 June 2020</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l49">Line 49:</td>
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<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>A positive rational number q belongs to the <del style="font-weight: bold; text-decoration: none;">[</del>pmin;pmax;fmin;fmax<del style="font-weight: bold; text-decoration: none;">]</del>-limit, called the '''prime-bounded and factor-bounded limit''', if q ∈ pmin-min-prime-limit ∩ pmax-max-prime-limit ∩ fmin-min-factor-limit ∩ fmax-max-factor-limit.</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>A positive rational number q belongs to the <ins style="font-weight: bold; text-decoration: none;">(</ins>pmin;pmax;fmin;fmax<ins style="font-weight: bold; text-decoration: none;">)</ins>-limit, called the '''prime-bounded and factor-bounded limit''', if q ∈ pmin-min-prime-limit ∩ pmax-max-prime-limit ∩ fmin-min-factor-limit ∩ fmax-max-factor-limit.</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>===Examples===</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>===Examples===</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;">[</del>5;7;0;3<del style="font-weight: bold; text-decoration: none;">]</del>-limit contains only 1/1, 5/1, 1/5, 5*5/1, 1/5*5, 5*5*5/1, 1/5*5*5, 7/1, 1/7, 5*7/1, 1/5*7, 7/5, 5/7, 7*7/1, 1/7*7, 5*5*7/1, 1/5*5*7, 7/5*5, 5*5/7, 5*7*7/1, 1/5*7*7, 7*7/5, 5/7*7, 7*7*7/1, 1/7*7*7</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;">(</ins>5;7;0;3<ins style="font-weight: bold; text-decoration: none;">)</ins>-limit contains only 1/1, 5/1, 1/5, 5*5/1, 1/5*5, 5*5*5/1, 1/5*5*5, 7/1, 1/7, 5*7/1, 1/5*7, 7/5, 5/7, 7*7/1, 1/7*7, 5*5*7/1, 1/5*5*7, 7/5*5, 5*5/7, 5*7*7/1, 1/5*7*7, 7*7/5, 5/7*7, 7*7*7/1, 1/7*7*7<ins style="font-weight: bold; text-decoration: none;">.</ins></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>* <del style="font-weight: bold; text-decoration: none;">[</del>5;13;0;2<del style="font-weight: bold; text-decoration: none;">]</del>-limit contains only 1/1, 5/1, 1/5, 5*5/1, 1/5*5, 7/1, 1/7, 5*7/1, 1/5*7, 7/5, 5/7, 7*7/1, 1/7*7, 11/1, 1/11, 5*11/1, 1/5*11, 11/5, 5/11, 7*11/1, 1/7*11, 11/7, 7/11, 11*11/1, 1/11*11, 13/1, 1/13, 5*13/1, 1/5*13, 13/5, 5/13, 7*13/1, 1/7*13, 13/7, 7/13, 11*13/1, 1/11*13, 13/11, 11/13, 13*13/1, 1/13*13</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;">(</ins>5;13;0;2<ins style="font-weight: bold; text-decoration: none;">)</ins>-limit contains only 1/1, 5/1, 1/5, 5*5/1, 1/5*5, 7/1, 1/7, 5*7/1, 1/5*7, 7/5, 5/7, 7*7/1, 1/7*7, 11/1, 1/11, 5*11/1, 1/5*11, 11/5, 5/11, 7*11/1, 1/7*11, 11/7, 7/11, 11*11/1, 1/11*11, 13/1, 1/13, 5*13/1, 1/5*13, 13/5, 5/13, 7*13/1, 1/7*13, 13/7, 7/13, 11*13/1, 1/11*13, 13/11, 11/13, 13*13/1, 1/13*13<ins style="font-weight: bold; text-decoration: none;">.</ins></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>* <del style="font-weight: bold; text-decoration: none;">[</del>5;31;0;1<del style="font-weight: bold; text-decoration: none;">]</del>-limit contains only 1/1, 5/1, 1/5, 7/1, 1/7, 11/1, 1/11, 13/1, 1/13, 17/1, 1/17, 19/1, 1/19, 23/1, 1/23, 29/1, 1/29, 31/1, 1/31</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;">(</ins>5;31;0;1<ins style="font-weight: bold; text-decoration: none;">)</ins>-limit contains only 1/1, 5/1, 1/5, 7/1, 1/7, 11/1, 1/11, 13/1, 1/13, 17/1, 1/17, 19/1, 1/19, 23/1, 1/23, 29/1, 1/29, 31/1, 1/31<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;">* (3;3;0;26)-limit contains only 3<sup>-26</sup>, 3<sup>-25</sup>, 3<sup>-24</sup>, 3<sup>-23</sup>, 3<sup>-22</sup>, 3<sup>-21</sup>, 3<sup>-20</sup>, 3<sup>-19</sup>, 3<sup>-18</sup>, 3<sup>-17</sup>, 3<sup>-16</sup>, 3<sup>-15</sup>, 3<sup>-14</sup>, 3<sup>-13</sup>, 3<sup>-12</sup>, 3<sup>-11</sup>, 3<sup>-10</sup>, 3<sup>-9</sup>, 3<sup>-8</sup>, 3<sup>-7</sup>, 3<sup>-6</sup>, 3<sup>-5</sup>, 3<sup>-4</sup>, 3<sup>-3</sup>, 3<sup>-2</sup>, 3<sup>-1</sup>, 1/1, 3<sup>1</sup>, 3<sup>2</sup>, 3<sup>3</sup>, 3<sup>4</sup>, 3<sup>5</sup>, 3<sup>6</sup>, 3<sup>7</sup>, 3<sup>8</sup>, 3<sup>9</sup>, 3<sup>10</sup>, 3<sup>11</sup>, 3<sup>12</sup>, 3<sup>13</sup>, 3<sup>14</sup>, 3<sup>15</sup>, 3<sup>16</sup>, 3<sup>17</sup>, 3<sup>18</sup>, 3<sup>19</sup>, 3<sup>20</sup>, 3<sup>21</sup>, 3<sup>22</sup>, 3<sup>23</sup>, 3<sup>24</sup>, 3<sup>25</sup>, 3<sup>26</sup>.</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;">* (2;2;0;+∞)-limit contains only 2<sup>0</sup>, 2<sup>1</sup>, 2<sup>-1</sup>, 2<sup>2</sup>, 2<sup>-2</sup>, 2<sup>3</sup>, 2<sup>-3</sup>, 2<sup>4</sup>, 2<sup>-4</sup>, 2<sup>5</sup>, 2<sup>-5</sup>, 2<sup>6</sup>, 2<sup>-6</sup>, 2<sup>7</sup>, 2<sup>-7</sup>, 2<sup>8</sup>, 2<sup>-8</sup>, 2<sup>9</sup>, 2<sup>-9</sup>, 2<sup>10</sup>, 2<sup>-10</sup>, 2<sup>11</sup>, 2<sup>-11</sup>, 2<sup>12</sup>, 2<sup>-12</sup>, 2<sup>13</sup>, 2<sup>-13</sup>, 2<sup>14</sup>, 2<sup>-14</sup>, 2<sup>15</sup>, 2<sup>-15</sup>, 2<sup>16</sup>, 2<sup>-16</sup>, 2<sup>17</sup>, 2<sup>-17</sup>, 2<sup>18</sup>, 2<sup>-18</sup>, 2<sup>19</sup>, 2<sup>-19</sup>, 2<sup>20</sup>, 2<sup>-20</sup>, etc...</ins></div></td></tr>
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Contribution
https://en.xen.wiki/index.php?title=User:Contribution/Factor_Limit&diff=47013&oldid=prev
Contribution: /* Definition */
2020-06-16T18:25:20Z
<p><span class="autocomment">Definition</span></p>
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<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 18:25, 16 June 2020</td>
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<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>A positive rational number q belongs to the fmin-min-factor-limit, called the '''minimal factor limit''', for a given positive integer fmin if and only if the sum of the exponent absolutes of its factorization into primes is more than or equal to fmin.</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>A positive rational number q belongs to the fmin-min-factor-limit, called the '''minimal factor limit''', for a given positive integer fmin if and only if the sum of the exponent absolutes of its factorization into primes is more than or equal to fmin.</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>In other words, a positive rational number q belongs to the fmin<del style="font-weight: bold; text-decoration: none;">-</del>-min-factor-limit if and only if the sum of the exponent absolutes of its factorization into primes is left-bounded to fmin.</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>In other words, a positive rational number q belongs to the fmin-min-factor-limit if and only if the sum of the exponent absolutes of its factorization into primes is left-bounded to fmin.</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>===Examples===</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>===Examples===</div></td></tr>
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Contribution