# Main Page

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− | ''Welcome to the | + | __NOTOC__{{DISPLAYTITLE:explain xkcd}} |

+ | <center> | ||

+ | <font size=5px>''Welcome to the '''explain [[xkcd]]''' wiki!''</font> | ||

− | + | We have collaboratively explained [[:Category:Comics|'''{{#expr:{{PAGESINCAT:Comics}}-9}}''' xkcd comics]], | |

+ | <!-- Note: the -9 in the calculation above is to discount subcategories (there are 8 of them as of 2013-02-27), | ||

+ | as well as [[List of all comics]], which is obviously not a comic page. --> | ||

+ | and only {{#expr:{{LATESTCOMIC}}-({{PAGESINCAT:Comics}}-9)}} | ||

+ | ({{#expr: ({{LATESTCOMIC}}-({{PAGESINCAT:Comics}}-9)) / ({{PAGESINCAT:Comics}}-9) * 100 round 0}}%) | ||

+ | remain. '''[[Help:How to add a new comic explanation|Add yours]]''' while there's a chance! | ||

+ | </center> | ||

+ | == Latest comic == | ||

+ | <div style="border:1px solid grey; background:#eee; padding:1em;"> | ||

+ | <span style="float:right;">[[{{LATESTCOMIC}}|'''Go to this comic explanation''']]</span> | ||

+ | <br clear="right"> | ||

+ | {{:{{LATESTCOMIC}}}} | ||

+ | {{#ifexist:Talk:{{LATESTCOMIC}}|<h2>Discussion</h2> | ||

+ | {{Talk:{{LATESTCOMIC}}}} | ||

+ | }}</div> | ||

− | + | <small>''Is this out of date? {{Purge|Clicking here will fix that}}.''</small> | |

− | + | ||

− | + | == New here? == | |

+ | You can read a brief introduction about this wiki at [[explain xkcd]]. Feel free to sign up for an account and contribute to the wiki! We need explanations for comics, characters, themes, memes and everything in between. If it is referenced in an [[xkcd]] web comic, it should be here. | ||

− | + | * If you're new to wikis like this, take a look at these help pages describing [[mw:Help:Navigation|how to navigate]] the wiki, and [[mw:Help:Editing pages|how to edit]] pages. | |

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− | + | * Discussion about various parts of the wiki is going on at [[Explain XKCD:Community portal]]. Share your 2¢! | |

− | + | * [[List of all comics]] contains a complete table of all xkcd comics so far and the corresponding explanations. The red links ([[like this]]) are missing explanations. Feel free to help out by creating them! [[Help:How to add a new comic explanation|Here's how]]. | |

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− | + | == Rules == | |

+ | Don't be a jerk. There are a lot of comics that don't have set in stone explanations; feel free to put multiple interpretations in the wiki page for each comic. | ||

− | + | If you want to talk about a specific comic, use its discussion page. | |

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− | If you | + | |

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− | + | Please only submit material directly related to —and helping everyone better understand— xkcd... and of course ''only'' submit material that can legally be posted (and freely edited.) Off-topic or other inappropriate content is subject to removal or modification at admin discretion, and users who repeatedly post such content will be blocked. | |

− | If you | + | If you need assistance from an admin, feel free to leave a message on their personal discussion page. The list of admins is [[Special:ListUsers/sysop|here]]. |

− | + | [[Category:Root category]] |

## Revision as of 05:35, 4 March 2013

*Welcome to the explain xkcd wiki!*

We have collaboratively explained **5** xkcd comics,
and only 1719
(34380%)
remain. **Add yours** while there's a chance!

## Latest comic

Proofs |

Title text: Next, let's assume the decision of whether to take the Axiom of Choice is made by a deterministic process ... |

## Explanation

Miss Lenhart is back teaching a math class. She begins a proof when one of her students (Cueball) interrupts her asking if this is one of those dark-magic (unclear, incomprehensible) proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.

The proof she starts setting up resembles a proof by contradiction. This kind of proof assumes that a particular theorem is true, and shows that this assumption leads to a contradiction, which disproves the initial assumption. For example assumption that √2 is a rational number means that, for some natural *a* and *b*, √2=*a/b*, where *a/b* is an irreducible fraction. But multiplying this equation by itself we get 2=*a²/b²*, which means that *a* is an even number. This means, that *a=2k* and *2b²=(2k)²=4k²*, so *b* must be even too. But if both *a* and *b* are even, *a/b* cannot be irreducible. Contradiction means that the initial assumption is false, and √2 cannot be a rational number.

The way, Ms Lenhart's proof refers to the act of proving itself, is characteristic to metamathematical proofs, for example Gödel's incompleteness theorems, which, at first sight, may indeed look like black magic, even if finally they must be a "perfectly sensible chain of resoning" like the rest of good mathematics. While standard mathematical theorems and their proofs deal with standard mathematical objects, like numbers, functions or curves, the metamathematical theorems treat other theorems as objects of interest. In this way you can propose and prove theorems about possibility of proving other theorems. For example, in 1931 Kurt Gödel was able to prove that any mathematical system based on arithmetics (that is using numbers) has statements that are true, but cannot be neither proved nor disproved. This kind of metamathematical reasoning is especially useful in the set theory, where many statements become impossible to prove and disprove if the axiom of choice is not taken.

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. The axiom of determinacy is incompatible with the axiom of choice, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in 804: Pumpkin Carving.

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 the her undergraduate class.

## Transcript

- [Miss Lenhart is standing facing left in front of a whiteboard writing on it. Eleven left aligned lines of writing is shown as unreadable scribbles. A voice interrupts her from off-panel right.]
- Miss Lenhart: ... Let's assume there exists some function
*F*(*a,b,c*...) which produces the correct answer- - Cueball (off-panel): Hang on.

- [In a frame-less panel Cueball is sitting on a chair at a desk with a pen in his hand taking notes.]
- Cueball: This is going to be one of those weird, dark magic proofs, isn't it? I can tell.

- [Miss Lenhart has turned right towards Cueball, who is again speaking off-panel. The white board is also off-panel.]
- Miss Lenhart: What? No, no, it's a perfectly sensible chain of reasoning.
- Cueball (off-panel): All right...

- [Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]
- Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the coordinates (
*x, y*). If we— - Cueball (off-panel): I
*knew*it!

*Is this out of date? *
.

## New here?

You can read a brief introduction about this wiki at explain xkcd. Feel free to sign up for an account and contribute to the wiki! We need explanations for comics, characters, themes, memes and everything in between. If it is referenced in an xkcd web comic, it should be here.

- If you're new to wikis like this, take a look at these help pages describing how to navigate the wiki, and how to edit pages.

- Discussion about various parts of the wiki is going on at Explain XKCD:Community portal. Share your 2¢!

- List of all comics contains a complete table of all xkcd comics so far and the corresponding explanations. The red links (like this) are missing explanations. Feel free to help out by creating them! Here's how.

## Rules

Don't be a jerk. There are a lot of comics that don't have set in stone explanations; feel free to put multiple interpretations in the wiki page for each comic.

If you want to talk about a specific comic, use its discussion page.

Please only submit material directly related to —and helping everyone better understand— xkcd... and of course *only* submit material that can legally be posted (and freely edited.) Off-topic or other inappropriate content is subject to removal or modification at admin discretion, and users who repeatedly post such content will be blocked.

If you need assistance from an admin, feel free to leave a message on their personal discussion page. The list of admins is here.