Sorry tried to formulate this question the other day, got myself into a bit of a pickle.
(By dense in [0,1] I mean there is an element in our set arbitrarily close to every point in [0,1]. If that isn't what dense in [0,1] means apologies.)
Some examples I have considered;
- The rationals (Countable, so no)
- The real line with the rationals removed (Measure 1 so no)
- Cantor set doesn't have anything within 1/6 of 0.5, right?
If not, does anyone know of a proof of the result?