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

Is it possible to simlify the follwing expression with a floor function:

$$\lim_{n\to \infty}\frac{1}{n}\left(\left\lfloor \frac{n\tau}{T}\right\rfloor-1\right)$$

share|cite|improve this question
Why the tag "probability-theory"? – Davide Giraudo Oct 11 '12 at 11:20
up vote 2 down vote accepted

For a real number $x$, $\lim_{n\to +\infty}\frac{\lfloor nx\rfloor}n=x$. Indeed, $$nx-1\leq\lfloor nx\rfloor\leq nx,$$ then we divide by $n$ and apply squeeze theorem.

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.