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!
\(\left |x \right | + \left |y \right | = \left |x \right | +\left |y \right |\)(1)
\(\left |x \right | + \left | y \right | \)>\(\left | x+y \right |\) (2)
\(\left |2x \right | + \left | 2y\right |\) >\(\left | x \right | + \left | y \right | +\left | x+y \right |\)
We prove it!
Hope it helps!
This is not what the guest wants to prove, I think you confused the floor function with the absolute value function
My attempt at a solution:
THANK YOU SOOOO MUCH GUYS! I really appreciate this. Thanks!
Side note: hmmm, i should probably make an account.
Side Side note: Oh, and my name is also Alan spelled the same way. Hehe