# Math Help - discrete math proof

1. ## discrete math proof

I need some urgent help on this question.

It says we have to prove that

floor of(5*x)- 5* (floor of x ) <4.1

I have been struggling this problem from past goddamn 6 hours :| wth

2. You have $\lfloor 5x\rfloor \leq 5x$ and $\lfloor x\rfloor > x-1$, hence $\lfloor 5x\rfloor - 5\lfloor x\rfloor < 5x - 5(x-1)=5$. Moreover, $\lfloor 5x\rfloor - 5\lfloor x\rfloor$ is an integer, so that the previous inequality is equivalent to $\lfloor 5x\rfloor - 5\lfloor x\rfloor\leq 4$.