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[0BS] For \(xβ β\) we define \(β x β\) to be the floor function defined as the greatest integer less than or equal to \(x\), as in
\[ β x β{\stackrel{.}{=}}\max \{ nββ€:nβ€ x\} \quad . \]
[0BS] For \(xβ β\) we define \(β x β\) to be the floor function defined as the greatest integer less than or equal to \(x\), as in