BIG O, BIG Omega,

In asymptotic analysis.

 

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

[tex]\sin(x)=x-\frac{x^3}{6}+O(x^5)[/tex]

 

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).

 

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