# BIG O, BIG Omega,

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?

Homework Helper
Gold Member
Dearly Missed
In asymptotic analysis.

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

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

Homework Helper
Gold Member
Dearly Missed
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).

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