User:Math site tester by nick/sandbox

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

Laconic
TODO: add laconic. https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714

Gödel's incompleteness theorems

https://www.lesswrong.com/posts/6wKf33az3bPh2WP55/goedel-incompleteness-for-dummies

https://www.lesswrong.com/posts/GZjGtd35vhCnzSQKy/godel-s-completeness-and-incompleteness-theorems

https://www.logicmatters.net/resources/pdfs/godelbook/GodelBookLM.pdf

Analogy
Cantor's diagonal argument but with (un)provable statements instead of (un)countable sets of numbers.

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

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

The First Theorem
TODO: add plain english

The Second Theorem
TODO: add plain english

Restatements
"TODO: copypaste/do-math-symbols-correctly for 'in this case' and 'the answer is' paragraphs from https://math.stackexchange.com/questions/453503/can-someone-explain-g%C3%B6dels-incompleteness-theorems-in-layman-terms"

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.