Medals and fanning if you give a detailed response!

Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$. Thank you! Detailed responses appreciated.

Question

Medals and fanning if you give a detailed response! 

Prove that $\lfloor 2x \rfloor + \lfloor 2y \rfloor \geq \lfloor x \rfloor + \lfloor y \rfloor + \lfloor x+y \rfloor$ for all real $x$ and $y$. Thank you! Detailed responses appreciated.

zmudz · Answer

just explain all your steps

anonymous · Answer

you directly copied from Yahoo answers... https://answers.yahoo.com/question/index?qid=20080601185619AAmivHm