Let $\nu \left( x \right) $ be the least number of steps that is required to construct a constructible length $x$, using compass and ruler in the well known fashion. Now, define the distance $d\left(x,y\right)$, of two constructible numbers $x$ and $y$ as the $\nu \left(|x -y|\right)$. Is this a metric for the space of all constructible numbers?
2026-03-29 20:49:47.1774817387
Ruler-and-Compass metric
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