This question already has an answer here:
- Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$ 3 answers
Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$.
If anybody could post a simple solution (no complicated abstract theories or calc :D) to the above question, I would greatly appreciate it. Thanks!
Also, if possible, the solution shouldn't wander too much away from floor, ceiling, fraction functions, and other related functions.