Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

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


How do I show this?

I made a plot, and it looks true:

share|cite|improve this question
up vote 8 down vote accepted

Hint: $\frac{x}{\lceil\sqrt{x}\rceil} \leq \lceil\frac{x}{\lceil\sqrt{x}\rceil}\rceil$.

share|cite|improve this answer
I of course assume that you're only considering $x \gt 0$. – t.b. Apr 16 '11 at 22:32

Divide both sides by $\lceil \sqrt x\rceil$.

share|cite|improve this answer

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.