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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…

> More surprisingly perhaps, if you colour the infinite subsets of the natural numbers red or blue, then there exist colourings for which there is no monochromatic subset. Could yo…

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 s…

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 co…

> 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 …

> Their age doesn't predict their accuracy. I was actually asking about the case where the demographic they're predicting the opinion of is age restricted -- are they good at predi…

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 …