Question 86
For a real number $x$, we denote by $\lfloor x\rfloor$ the greatest integer less than or equal to $x$ (for example, $\lfloor 2.7\rfloor=2$, $\lfloor\pi\rfloor=3$ and $\lfloor-1.5\rfloor=-2$).
Let $a, b$ be two real numbers such that
$$
a+\lfloor a\rfloor=b+\lfloor b\rfloor .
$$
Show that $a=b$.
Let $a, b$ be two real numbers such that
$$
a+\lfloor a\rfloor=b+\lfloor b\rfloor .
$$
Show that $a=b$.