Editing 982: Set Theory
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| title = Set Theory | | title = Set Theory | ||
| image = set_theory.png | | image = set_theory.png | ||
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| titletext = Proof of Zermelo's well-ordering theorem given the Axiom of Choice: 1: Take S to be any set. 2: When I reach step three, if S hasn't managed to find a well-ordering relation for itself, I'll feed it into this wood chipper. 3: Hey, look, S is well-ordered. | | titletext = Proof of Zermelo's well-ordering theorem given the Axiom of Choice: 1: Take S to be any set. 2: When I reach step three, if S hasn't managed to find a well-ordering relation for itself, I'll feed it into this wood chipper. 3: Hey, look, S is well-ordered. | ||
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==Explanation== | ==Explanation== | ||
| − | This comic is a pun on the phrase "{{w|Proof by Intimidation}}" which normally | + | This comic is a pun on the phrase "{{w|Proof by intimidation|Proof by Intimidation}}" which normally means ''a jocular term used mainly in mathematics to refer to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeal to obscure results, so that the audience is simply obliged to accept it, lest they have to admit their ignorance and lack of understanding''. |
| − | However, in this comic, "Proof by Intimidation" is taken to mean that by intimidating the elements within a set, they will conform to the proof (or, as the title text says, they will become "well-ordered"). This is accomplished by believing that the elements can be {{w|anthropomorphize}}d such that they feel fear. The idea of executing as an example was | + | However, in this comic, "Proof by Intimidation" is taken to mean that by intimidating the elements within a set, they will conform to the proof (or, as the title text says, they will become "well-ordered"). This is accomplished by believing that the elements can be {{w|anthropomorphize}}d such that they feel fear. The idea of executing as an example was invented by Sun Tzu in the ancient book {{w|The Art Of War}}. |
| − | + | The {{w|axiom of choice}} (which has been referenced in [[:Category:Axiom of Choice|previous xkcds]]) says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin. | |
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| − | + | In the title text, the well-ordering theorem states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. This is also known as {{w|Zermelo's theorem}} and is equivalent to the Axiom of Choice. | |
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| − | In the title text, the well-ordering theorem states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. This is also known as {{w|Zermelo's theorem}} and is equivalent to the Axiom of Choice | ||
==Transcript== | ==Transcript== | ||
| − | + | [A woman with a ponytail stands at a blackboard, facing away from it. She has a pointer in her hand, and written on the blackboard is some set theory math.] | |
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| − | : | + | Woman: The axiom of choice allows you to select one element from each set in a collection — and have it ''executed'' as an example to the others. |
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| − | + | My math teacher was a big believer in Proof by Intimidation. | |
| + | {{comic discussion}} | ||
[[Category:Comics featuring Ponytail]] | [[Category:Comics featuring Ponytail]] | ||
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| + | [[Category:Axiom of Choice]] | ||
[[Category:Math]] | [[Category:Math]] | ||
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