https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&feed=atom&action=history1724: Proofs - Revision history2024-03-29T07:16:57ZRevision history for this page on the wikiMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=312465&oldid=prev172.69.70.228: /* Explanation */2023-05-06T11:38:11Z<p><span dir="auto"><span class="autocomment">Explanation</span></span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 11:38, 6 May 2023</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Using a position on the blackboard as a part of the proof is a joke, but it bears a resemblance to {{w|Cantor's diagonal argument}} where a position in a sequence of digits of a real number was a tool in a proof that not all infinite sets have the same {{w|cardinality}} (rough equivalent of the number of elements). This "diagonal method" is also often used in metamathematical proofs.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>The axiom of choice itself states that for every collection of nonempty sets, you can have a function that draws one element from each set of the collection. This axiom, once considered controversial, was added relatively late to the axiomatic set theory, and even contemporary mathematicians still study which theorems really require its inclusion. In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. {{w|Determinacy}} of infinite games is used as a tool in the set theory, however the deterministic process is rather a term of the {{w|stochastic process|stochastic processes theory}}, and the {{w|dynamical systems theory}}, branches of mathematics far from the abstract set theory, which makes the proof even more exotic. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]] and later in [[982: Set Theory]], another comic about a math class with a similar theme on how teachers teach their student mathematical proofs.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>The axiom of choice itself states that for every collection of <ins class="diffchange diffchange-inline">disjoint </ins>nonempty sets, you can have a function that draws one element from each set of the collection. This axiom, once considered controversial, was added relatively late to the axiomatic set theory, and even contemporary mathematicians still study which theorems really require its inclusion. In the title text the decision of whether to take the axiom of choice is made by a deterministic process, that is a process which future states can be developed with no randomness involved. {{w|Determinacy}} of infinite games is used as a tool in the set theory, however the deterministic process is rather a term of the {{w|stochastic process|stochastic processes theory}}, and the {{w|dynamical systems theory}}, branches of mathematics far from the abstract set theory, which makes the proof even more exotic. The axiom of choice was mentioned earlier in [[804: Pumpkin Carving]] and later in [[982: Set Theory]], another comic about a math class with a similar theme on how teachers teach their student mathematical proofs.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class. A very similar Miss Lenhart comic was later released with [[2028: Complex Numbers]].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Although Miss Lenhart did retire a year ago after [[1519: Venus]], she seems to have returned here for a math course at university level, but continues the trend she finished with in her prior class. A very similar Miss Lenhart comic was later released with [[2028: Complex Numbers]].</div></td></tr>
</table>172.69.70.228https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=257404&oldid=prevJacky720: rv2022-05-04T22:37:52Z<p>rv</p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=257404&oldid=254073">Show changes</a>Jacky720https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=254073&oldid=prevEx Kay Cee Dee at 22:14, 4 May 20222022-05-04T22:14:56Z<p></p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=254073&oldid=253860">Show changes</a>Ex Kay Cee Deehttps://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=253860&oldid=prevEx Kay Cee Dee at 22:13, 4 May 20222022-05-04T22:13:03Z<p></p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=253860&oldid=252269">Show changes</a>Ex Kay Cee Deehttps://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=252269&oldid=prevJacky720: rv2022-05-04T22:00:04Z<p>rv</p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=252269&oldid=252265">Show changes</a>Jacky720https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=252265&oldid=prevEx Kay Cee Dee at 22:00, 4 May 20222022-05-04T22:00:01Z<p></p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=252265&oldid=250623">Show changes</a>Ex Kay Cee Deehttps://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=250623&oldid=prevJacky720: rv2022-05-04T21:46:04Z<p>rv</p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=250623&oldid=250618">Show changes</a>Jacky720https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=250618&oldid=prevEx Kay Cee Dee at 21:46, 4 May 20222022-05-04T21:46:03Z<p></p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=250618&oldid=246135">Show changes</a>Ex Kay Cee Deehttps://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=246135&oldid=prevJacky720: rv2022-05-04T21:03:50Z<p>rv</p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=246135&oldid=243745">Show changes</a>Jacky720https://www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=243745&oldid=prevEx Kay Cee Dee at 20:36, 4 May 20222022-05-04T20:36:54Z<p></p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1724:_Proofs&diff=243745&oldid=243245">Show changes</a>Ex Kay Cee Dee