題組內容

1. Consider the function f(x) = [x] - [x], where [x] denotes the smallest integer that is greater than or equal to x, and [x] denotes the greatest integer that is smaller than or equal to x. (That is, [x] = \( n \in \mathbb{Z} \) , and \( \lfloor x \rfloor = m \in \mathbb{Z} \) such that m ≤ x < m + 1.)

1.1      (3%)      True or False: The function \( f(x) \) is an increasing function.