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Jun 3, 2017 at 21:45 comment added Bob Krueger Once you have said "without loss of generality" you have broken the symmetry, and can no longer argue with this nonexistent symmetry.
Jun 2, 2017 at 21:07 comment added pigeon whole I was thinking how the first condition cannot be satisfied if you already have $3$ elements. Since every $3$-tuple gets a color, assume in this case it gets blue, but using the symmetry of the relation (in the last line) we can swap colors, and done. Or does the symmetry only holds for $2$-tuples ?
Jun 2, 2017 at 18:40 history answered Bob Krueger CC BY-SA 3.0