Question

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! I've tried using \(n \le x < n+1\) when \(\lfloor x \rfloor = n\). Not sure what to do next. Detailed response appreciated!

Answer 1

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