Kenneth Rosen Edition 7 Exercise 2.3 Question 51 (Page No. 154)

Question

Show that if $x$ is a real number and $n$ is an integer, then

1. $x<n$ if and only if $\left \lfloor x \right \rfloor < n$
2. $n<x$ if and only if $ n<=\left \lfloor x \right \rfloor $