Given:
- $Floor(x)=\lfloor x \rfloor$
- $Ceiling(x)=\lceil x \rceil$
Where $x$ is a real number.
Is there any other (mathematical) way for defining $Floor(x)$ and $Ceiling(x)$?
Restrictions:
- Do not use the Floor function in order to define the Ceiling function.
- Do not use the Ceiling function in order to define the Floor function.
- Do not use the Round function in order to define either one of them.
Please excuse the possible duplicate, as I haven't been able to do find this question anywhere...
Thanks