This lemma was known (or perhaps more accurately "suspected") since the middle ages, but only in the 19th century did Kronecker formulate and prove it. In fact, the considerably stronger Weyl's lemma is true of the fractional part of irrational rotations.

**Lemma.**
Let `a` be an irrational number. Then the set of all numbers of the form
{`n a`} := `n a` - [`n a`]

(where [`x`] is the largest integer not greater than `x`) is dense in the interval [0,1].