Set theory

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“Here, here! I know one! Here it goes: Are cardinals countable? Now... lets see: Richelieu, Wolsey, Borgia... [laughs] Wait, wait! I have more of them! What do you get if you put all cardinals into one set? A paradox!”
~ Oscar Wilde on Set theory

“What the f..? What a nerd.”
~ Sun-Tzu on Oscar Wilde on Set theory

“I think he's dreamy. He could set my theory any day...”
~ your mom on Oscar Wilde on Set theory

Set theory is an obscure strain of mathematics. It is the study of things which may potentially contain other things. It is further theorized, through the principle of induction, that these contained things, in turn, may contain yet other things. Also, the contained things which are contained inside the previously mentioned contained things may yet contain other contained things that contain even more contained containers that may or may not reference themselves among other things. However, these things may not contain themselves, as that would just be plain silly.

edit The Golden Age of Naïvety

During the Golden Age of Naïvety, you could put whatever you jolly well pleased into a set. But unfortunately, this unrestrained licentiousness led to a massive boycott by the barbers of the world, who weren't quite able to figure out if they themselves were supposed to be included inside their own sets or not. And thus a massive government regulation process began.

edit Government Regulation

In 1908, Senator Ernst Zermelo drafted the AXIOM Act: a set of government-enforced regulations which attempted to protect the world from the deadly barberous threat. The laws were as follows:

  • Law of Equivocation: Two sets which contain the same items must be advertised as equal products.
  • Law of Civil Unions: If two sets love each other very much, they are permitted to form a pair and have a civil union. However, unionized sets were forbidden to divorce each other, as that was a grievous sin in the eyes of the LORD.
  • Law of Replacement, or your Money Back: All stores must be guaranteed to stock every individual item from the ever-popular set Natural N. Stores must allow people to pick and choose whatever they want to keep in their personal sets, and also allow people to replace any item in a set for another item of equal or lesser value.
  • Law of Supersizing: Stores must also offer a Power Set version of every set which they sell. This is largely due to the efforts of hip trendsetter Georg Cantor in popularizing the Power Set.
  • Law of Regularity: All sets must contain the daily recommended dosage of fiber (later, sets bundled with fiber came to be known as fiber bundles). Regularity is the foundation of a healthy lifestyle.

edit Constitutional Aspects

edit Axiom of Choice

Main article: Axiom of Choice

In 1973, the Supreme Court ruled that women have a constitutional right to choose; and that as a result, a woman may freely take individual items out of her own personal set. This ruling was extremely controversial at the time, but fortunately, women aren't mathematicians.

Two pro-life mathematicians, Hahn Banach and Alfred Tarski, showed that allowing choice leads to the counter-intuitive result that a solid ball can be decomposed without stretching, then the pieces can be put together to form two solid balls each of the same size as the original. In response, leading feminists have declared that they are "happy to decompose the balls of Banach and Tarski at any time".

In order to confuse opponents of choice, Max August Zorn formulated what came to be known as Zorn's lemma. Since this lemma is painfully difficult for non-mathematicians to understand, they are prone to accepting it purely to make you go away. However, it is known that Zorn's lemma is actually equivalent to choice. Zorn's lemma is therefore widely recognized for its role in the Supreme Court fight over women's right of choice.

edit Axiom of Determinacy

French mathematicians such as Baire, Borel and Lebesgue are known to be foes of choice. Instead, they prefer the Axiom of Dependent Choice:

Axiom of Dependent Choice. Women's right to choice should be dependent on their male guardians.

However, this axiom offended both pro-choice and pro-life activists, although the French analysts do not care because they are French. Polish-American mathematicians Mycielski and Steinhaus, on the other hand, being Poles and unable to afford pissing off the wrong type of people, formulated the Axiom of Determinacy:

Axiom of Determinacy. Whether a fetus will be carried to term is solely determined by God.

Because this axiom is so vague, neither the pro-choice nor the pro-life crowd knew what to do about it, so they left the authors alone.

edit See Also

Ready Theory
Set Theory Next:
Go Theory
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