Real Number is between Floor Functions

Theorem

 * $$\forall x \in \R: \left \lfloor {x} \right \rfloor \le x < \left \lfloor {x + 1} \right \rfloor$$

where $$\left \lfloor {x} \right \rfloor$$ is the floor of $$x$$.

Proof
Follows directly from Range of Values of Floor Function: Result 4:


 * $$\left \lfloor{x}\right \rfloor = n \iff n \le x < n + 1$$