Real Number is between Ceiling Functions

Theorem

 * $$\forall x \in \R: \left \lceil {x - 1} \right \rceil \le x < \left \lceil {x} \right \rceil$$

where $$\left \lceil {x} \right \rceil$$ is the ceiling of $$x$$.

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


 * $$\left \lceil{x}\right \rceil = n \iff n - 1 \le x \le n$$