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

@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!"

@Scmbradley Harder to express cleanly.

It's an interesting observation and starting point though.

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