Answer
see step by step
Work Step by Step
We can write the real number x as l x J + t, where t is a real number satisfying 0 ~ t < 1. Since t = x - l x J ,
we have 0 ~ x - l x J < 1. The first two inequalities, x - 1 < l x J and l x J ~ x, follow algebraically. For the
other two inequalities, we can write x = r x l - E, where again 0 ~ E < 1. Then 0 ~ r x l - x < 1, and again
the desired inequalities follow by easy algebra.
