Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
up vote 3 down vote accepted

HINT: Let $m=\lfloor x\rfloor$ and $n=\lfloor y\rfloor$, so that $m\le x<m+1$ and $n\le y<n+1$. Then $$m+n\le x+y< m+n+2\;;$$ can you finish it from there?

share|cite|improve this answer
@cth: There’s almost nothing left. Those inequalities leave only two possibilities for $\lfloor x+y\rfloor$. – Brian M. Scott Mar 13 '15 at 22:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.