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.

Please provide a full solution. Thanks!

Guest Oct 18, 2018

#1**+1 **

\(\left |x \right | + \left |y \right | = \left |x \right | +\left |y \right |\)(1)

We know:

\(\left |x \right | + \left | y \right | \)__>__\(\left | x+y \right |\) (2)

We (1)+(2)

\(\left |2x \right | + \left | 2y\right |\) __>__\(\left | x \right | + \left | y \right | +\left | x+y \right |\)

We prove it!

Hope it helps!

Dimitristhym
Oct 18, 2018

#2**0 **

This is not what the guest wants to prove, I think you confused the floor function with the absolute value function

Guest Oct 18, 2018

#3**0 **

Oh now i see it.It's 8:57 a.m. and im awake all night I was studying.I'm sorry!

Thanks for the observation!

Dimitristhym
Oct 18, 2018