Wouldn't the subset {(a, b) | a,b > 20} be monochromatic? Ed: Perhaps I phrased it poorly, but I think the point was to show that you can always construct a predicate, P over a and b, such that P(a, b) is finitely…
The hard part is to show that for any coloring, there's some infinite subset without relying on "well, we can just pick one for each of these infinitely many numbers". I'm pretty sure that the challenge is to prove that…
Imagine you have one person for each (positive) integer, given a unique integer ID at birth, and a hotel with countably infinite rooms, each with a unique room number. The hotel could have someone in everyone room if…
> Job seekers are much better served spending an hour sending 10 focused applications than spending that same hour to send 100 sanitized applications. Let's assume that you have a 1 in 20 chance on the focused…
This might be an off topic question, but how do the results change (if at all) when accounting for the age of the people involved? That is, how do politicians do at predicting the opinions of people +/- 5 years of their…
Wouldn't the subset {(a, b) | a,b > 20} be monochromatic? Ed: Perhaps I phrased it poorly, but I think the point was to show that you can always construct a predicate, P over a and b, such that P(a, b) is finitely…
The hard part is to show that for any coloring, there's some infinite subset without relying on "well, we can just pick one for each of these infinitely many numbers". I'm pretty sure that the challenge is to prove that…
Imagine you have one person for each (positive) integer, given a unique integer ID at birth, and a hotel with countably infinite rooms, each with a unique room number. The hotel could have someone in everyone room if…
> Job seekers are much better served spending an hour sending 10 focused applications than spending that same hour to send 100 sanitized applications. Let's assume that you have a 1 in 20 chance on the focused…
This might be an off topic question, but how do the results change (if at all) when accounting for the age of the people involved? That is, how do politicians do at predicting the opinions of people +/- 5 years of their…