Can I prescribe a V shape to every number on the real number line so that the point of the V is in contact with this number, and no two V shapes intersect? (You may choose any specifically shaped "V" for each number, change the width of the V's, change the length of the legs of the V's, place V's in in the upper half-plane or lower half-plane)
2026-05-06 03:16:41.1778037401
Prescribing V shapes to the real numbers
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I'm afraid not. Every V shape (when filled in) contains a rational point, and there are only countably many of those, but there are uncountably many reals, so at least one point is shared between two filled-in V's. Now show that those two V's intersect at an edge.