/sci/ - Science & Math

>>14952729
[math]\displaystyle \lim_{n \to \infty} \dfrac{nb - 1}{n} = \lim_{n \to \infty} \dfrac{nb}{n} + \lim_{n \to \infty} \dfrac{1}{n} = b[/math]
[math]\displaystyle b = \lim_{n \to \infty} \dfrac{nb - 1}{n} \leq \lim_{n \to \infty} \dfrac{\lfloor nb \rfloor }{b} \leq \lim_{n \to \infty} \dfrac{nb}{b} = b[/math]