Take the 2-minute tour ×
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.

Given a positive and increasing sequence $\{a_n\}$, what is the meaning of $a_n$ grows as for example $O(n\log n)$ or $O(n^2)$. I have read this in some books but the google search did not yield anything.

share|improve this question
add comment

2 Answers

up vote 3 down vote accepted

Actually this is the Big O or Landau-Notation which is explained here. In this example you can define a function

$$f: \mathbb{N} \longrightarrow \mathbb{R}, f(n):=a_n$$

and for example $a_n$ grows $O(n^2)$ now means that there are constants $k, n_0$ such that $$\forall n>n_0 \; |f(n)| \leq |n^2\cdot k|$$

share|improve this answer
2  
I would have said: $|f(n)| \le k\;n^2$. –  GEdgar Jun 11 '11 at 16:54
    
I am sorry you are right of course I was confused with tex :-) –  Listing Jun 11 '11 at 16:59
add comment

Please see this Wikipedia article.

share|improve this answer
add comment

Your Answer

 
discard

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.