User:IssaRice/Schröder–Bernstein theorem: Difference between revisions
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* are the ancestor proof and the iterated partition proof actually different, or do they just look different on the surface? btw [https://www.cs.cornell.edu/courses/cs2800/2017sp/lectures/lec05-cantor.html this] is a very nice writeup of the ancestor proof (much clearer than wikipedia's version); HT Satira. | * are the ancestor proof and the iterated partition proof actually different, or do they just look different on the surface? btw [https://www.cs.cornell.edu/courses/cs2800/2017sp/lectures/lec05-cantor.html this] is a very nice writeup of the ancestor proof (much clearer than wikipedia's version); HT Satira. UPDATE: these are actually basically the same proof, just written in different notation. | ||
* what is the proof that uses axiom of choice, and how does choice simplify the proof? | * what is the proof that uses axiom of choice, and how does choice simplify the proof? | ||
* is the result a fixed point result? (if so how can we phrase it as such?) or is it just that some of the proofs makes use of the fixed point ideas? | * is the result a fixed point result? (if so how can we phrase it as such?) or is it just that some of the proofs makes use of the fixed point ideas? | ||
==References== | |||
* https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem | |||
* https://www.cs.cornell.edu/courses/cs2800/2017sp/lectures/lec05-cantor.html | |||
* http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf#page=242 | |||
* https://math.stackexchange.com/questions/3323133/questions-about-the-schroeder-bernstein-theorem | |||
* https://proofwiki.org/wiki/Cantor-Bernstein-Schr%C3%B6der_Theorem/Lemma | |||
* https://proofwiki.org/wiki/Cantor-Bernstein-Schr%C3%B6der_Theorem | |||
Revision as of 02:59, 30 August 2020
questions:
- are the ancestor proof and the iterated partition proof actually different, or do they just look different on the surface? btw this is a very nice writeup of the ancestor proof (much clearer than wikipedia's version); HT Satira. UPDATE: these are actually basically the same proof, just written in different notation.
- what is the proof that uses axiom of choice, and how does choice simplify the proof?
- is the result a fixed point result? (if so how can we phrase it as such?) or is it just that some of the proofs makes use of the fixed point ideas?
References
- https://en.wikipedia.org/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem
- https://www.cs.cornell.edu/courses/cs2800/2017sp/lectures/lec05-cantor.html
- http://www.people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf#page=242
- https://math.stackexchange.com/questions/3323133/questions-about-the-schroeder-bernstein-theorem
- https://proofwiki.org/wiki/Cantor-Bernstein-Schr%C3%B6der_Theorem/Lemma
- https://proofwiki.org/wiki/Cantor-Bernstein-Schr%C3%B6der_Theorem