I am trying to prove $$2\lfloor x\rfloor \le \lfloor2x\rfloor$$ which in turn will yield a prove for a homework question. I thought it is a simple prove but I can't figure it out. Maybe it is just a simple thing I overlooked. Any help?
I tried to use $x - \lfloor x\rfloor \ge 0$ to prove $2\lfloor x\rfloor-\lfloor2x\rfloor \le 0$ with no success.