Understanding a question in algebra

Question

Does the equality $\lfloor nx \rfloor = n\lfloor x \rfloor$ hold for the integers $n\ge 2$?

What does this sign "$\lfloor$" and " $\rfloor$" sign mean in this context?

Thanks!

Answer 1

$\lfloor x \rfloor$ denotes the largest integer not more than $x$, where $x$ is any real number. For example, $\lfloor 13 \rfloor=13$, $\lfloor 22.2 \rfloor=22$ and $\lfloor -\pi \rfloor=-4$.

Now, to answer your original question, let $x=\dfrac{1}{n}$. Then, $\lfloor nx \rfloor=\lfloor 1 \rfloor=1$, but $n\lfloor x \rfloor=n\cdot 0=0$. Hence, the statement does not hold.