Colin Hayman wrote: > > > Joseph levine wrote: > > > Does there exist a subset of the unit square such that all horizontal > > > lines intersect the set in countably many points but all vertical > > > lines intersect the set in uncountably many points? > > > > ((x, y): x rational, 0 < x,y < 1) would seem to be a trivial solution. > > That was one of my first thoughts, but consider the vertical line x = > 1/pi. Any point on that line has an irrational x-coordinate between 0 and > 1 (namely 1/pi), so it doesn't contain any points from your subset -- and > zero is about as countable as it gets.
Thanks, I suspected I had to be missing something.