\begin{definition}[Definition:Beatty Sequence]
Let $x$ be an irrational number.
The '''Beatty sequence on $x$''' is the integer sequence $\BB_x$ defined as:
:$\BB_x := \sequence{\floor{n x} }_{n \mathop \in \Z_{\ge 0} }$
That is, the terms are the floors of the successive integer multiples of $x$.
\end{definition}