If $1 > a-b > 0$ then $[a]\geq[b]$

Question

what I can do for The case $[a]<[b]$.

I know that $[a]>[b]\Rightarrow [a]\geq [b]+1$

EDIT:

I have realized that the Initial assumption $[a]=[b]$ is false therefore I have changed it to $[a]\geq [b]$

Answer 1

If $a \geq b$ then it immediately follows that $\lfloor a \rfloor \geq \lfloor b\rfloor$. So we don't even need the upper bound.

(All this says is that the floor function is monotone increasing.)