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.
This comic is a pun on the phrase "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 anthropomorphized such that they feel fear. This interpretation of the term "Proof by Intimidation" bears great resemblance to argument from the stick, which is a fallacious form of reasoning of the form:
1. If not P, I will do you harm.
2. Therefore, P.
This form of fallacy has the distinction, if properly applied, of never being called out as fallacious. Ponytail, however, is threatening the proposition itself, rather than her audience, bringing a level of absurdity to the situation.The 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 Zermelo's theorem and is equivalent to the Axiom of Choice. The woodchipper is a reference to the 1996 film Fargo, where a character uses one to dispose of a body.