Nice argument! (and thank you for the compliment)
Quote:
Originally Posted by Elroch
There is a nontrivial linear relation on these points:
Rearrange so all the coefficients are positive (changing labels for convenience)
and must be nonempty subsets of because the relation is nontrivial, and the first coordinate of all the points is 1.

Just to elaborate, the coefficients are not all zeros so because of the constant 1 coordinate, there has to be at least one positive and one negative coefficient, hence the rest of the argument even if all other coefficients are zeros.