User:Math site tester by nick/sandbox
Gödel's incompleteness theorems[edit]
Gödel's incompleteness theorems are two theorems in mathematical logic.
The quick version[edit]
Laconic[edit]
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[edit]
Cantor's diagonal argument but with (un)provable statements instead of (un)countable sets of numbers.
Visuals[edit]
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[edit]
TODO: add one or more examples/story problems
Longer Explanation[edit]
Historical Motivation[edit]
TODO: add why they needed/used/came up with this
Plain English[edit]
The First Theorem[edit]
TODO: add plain english
The Second Theorem[edit]
TODO: add plain english
Restatements[edit]
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 Definition[edit]
Technical[edit]
TODO: describe in technical language
Proof[edit]
TODO: add links to Godel's and proofs from https://arxiv.org/abs/1612.02549
Metamath[edit]
TODO: somebody fill the issue https://github.com/metamath/set.mm/issues/87, link resulting MM file.
Flashcards[edit]
TODO: create Anki deck once page is semi-complete.
Practice Problems[edit]
TODO: create practice problems once page is semi-complete.