# BIG O, BIG Omega,

1. Oct 6, 2006

### Swapnil

Hi, I was wondering, do mathematicians (like computer scientists) use things like Big O, Big Omega, Little O, etc. a lot? If so, in what context?

2. Oct 6, 2006

### arildno

In asymptotic analysis.

3. Oct 6, 2006

### CRGreathouse

Yep, asymptotic analysis accounts for most of it. It's also used to show the truncation of a (Taylor series) polynomial:

$$\sin(x)=x-\frac{x^3}{6}+O(x^5)$$

4. Oct 6, 2006

### arildno

And isn't that, really, an expression for sin(x)'s asymptotic behaviour as x ambles peacefully off towards the origin?

(If you write sin(x) with an explicit remainder term, say, by utilization of the mean-value theorem for integrals, then it is of course something different, but we wouldn't use O's in that case).

Last edited: Oct 6, 2006
5. Oct 7, 2006

### CRGreathouse

Oh yes absolutely. It's just a different way of thinking about it.