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Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems in mathematical logic.

The quick version

Laconic

TODO: add laconic.

Analogy

TODO: add analogy

Visuals

https://www.youtube.com/watch?v=HeQX2HjkcNo TODO: embed these as https://www.mediawiki.org/wiki/Extension:YouTube

https://www.youtube.com/watch?v=YrKLy4VN-7k

The visual here (and caveats described): https://math.stackexchange.com/questions/1319459/is-this-visual-analogy-to-g%C3%B6dels-incompleteness-theorem-accurate

Examples

TODO: add one or more examples/story problems

Longer Explanation

Historical Motivation

TODO: add why they needed/used/came up with this

Plain English

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Technical Definition

Technical

TODO: describe in technical language

Proof

TODO: add links to Godel's and proofs from https://arxiv.org/abs/1612.02549

Metamath

TODO: somebody fill the issue https://github.com/metamath/set.mm/issues/87, link resulting MM file.

Flashcards

TODO: create Anki deck once page is semi-complete.

Practice Problems

TODO: create practice problems once page is semi-complete.