The irrationals are those exactly those reals that are a different distance from every rational.

@ColinTheMathmo Trippy. But makes sense!

@ColinTheMathmo even more: no integer multiple of a distance to some rational is the same as the distance to another rational.

(I'm not sure I expressed that well...)

@Scmbradley @ColinTheMathmo if you want to express it more succinctly:

"Integers? We don't need your steenking integers!"