Mathematicians & Big O, Big Omega: Usage & Context

[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?

 

[arildno]

In asymptotic analysis.

 

[CRGreathouse]

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

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

 

[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).

 

[CRGreathouse]

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

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