If $x,y\in\mathbb R$, I have problems to show that
$$\lfloor x\rfloor+\lfloor y\rfloor\le \lfloor x+y\rfloor\le \lfloor x\rfloor+\lfloor y\rfloor + 1 $$
Can someone help me?
If $x,y\in\mathbb R$, I have problems to show that
$$\lfloor x\rfloor+\lfloor y\rfloor\le \lfloor x+y\rfloor\le \lfloor x\rfloor+\lfloor y\rfloor + 1 $$
Can someone help me?
HINT: Let $m=\lfloor x\rfloor$ and $n=\lfloor y\rfloor$, so that $m\le x