Editing 982: Set Theory
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.
The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
| Latest revision | Your text | ||
| Line 10: | Line 10: | ||
This comic is a pun on the phrase "{{w|Proof by Intimidation}}" which normally is a jocular term used mainly in mathematics. It refers to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeals to obscure results, so that the audience is simply obliged to accept it, lest they have to admit to their ignorance and lack of understanding. | This comic is a pun on the phrase "{{w|Proof by Intimidation}}" which normally is a jocular term used mainly in mathematics. It refers to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeals to obscure results, so that the audience is simply obliged to accept it, lest they have to admit to 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 exemplified by Sun Tzu in the ancient book {{w|The Art Of War}}. |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
The {{w|axiom of choice}} (which has been referenced previously in [[804: Pumpkin Carving]]) 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. It was later referenced in the title text of [[1724: Proofs]], another comic about a math class with a similar theme on how teachers teach their student mathematical proofs. | The {{w|axiom of choice}} (which has been referenced previously in [[804: Pumpkin Carving]]) 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. It was later referenced in the title text of [[1724: Proofs]], another comic about a math class with a similar theme on how teachers teach their student mathematical proofs. | ||
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. The woodchipper is a reference to the 1996 film {{w|Fargo (film)|Fargo}}, where a character uses one to dispose of a body. | 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. The woodchipper is a reference to the 1996 film {{w|Fargo (film)|Fargo}}, where a character uses one to dispose of a body. | ||
| + | |||
| + | It might seem there is another layer to the joke: if you can feed the set to the wood-chipper, that defines an ordering on the set (the order in which the elements are fed to the wood chipper). However, that doesn't actually work, because the resulting ordering is not necessarily well-ordered. For example, consider the set of positive real numbers. You can imagine feeding half a number line to a wood chipper from the end near zero. This defines the standard less-than ordering, but it is not a well-ordering because it does not define a least element. For any positive number x, x/2 went into the wood chipper first. The set may be motivated to find a well-ordering, but it won't be the standard one. | ||
==Transcript== | ==Transcript== | ||
| Line 25: | Line 22: | ||
:Ponytail: The axiom of choice allows you to select one element from each set in a collection | :Ponytail: The axiom of choice allows you to select one element from each set in a collection | ||
:Ponytail: and have it ''executed'' as an example to the others. | :Ponytail: and have it ''executed'' as an example to the others. | ||
| − | |||
| − | |||
:My math teacher was a big believer in Proof by Intimidation. | :My math teacher was a big believer in Proof by Intimidation. | ||
