4 ms·

What is it you like about the proof?

• eindiran 7y ago
  There is a section that uses the same type of thinking that you can use to prove the R(3, 3) = 6 case (often known as the Theorem of Friends and Strangers [0]), towards the end of the paper [1] (though in a pretty different way). Proving the general case of things is often very removed from the proofs of a specific case, so its interesting to see similar thinking in the general case. Also, I really like the simplicity of the proof of the Theorem of Friends and Strangers. You can show someone the proof with two colored pens in 10 minutes. But at the same time, it uses some interesting proof tools: contradiction, the pidgeonhole principle, creating a boundary by counterexample (ie that R(3, 3) must be greater than 5). So I like the Friends and Strangers proof for its elegance and how fun it is to show people, and I like Ramsey's proof because it captures some of the fun of the R(3, 3) case while proving something much, much more difficult. [0] https://en.wikipedia.org/wiki/Theorem_on_friends_and_strangers https://en.wikipedia.org/wiki/Theorem_on_friends_and_strange... [1] https://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseyorig.pdf https://www.cs.umd.edu/~gasarch/BLOGPAPERS/ramseyorig.pdf