BIG O, BIG Omega,

  • Thread starter Swapnil
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  • #1
Swapnil
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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?
 

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  • #2
arildno
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In asymptotic analysis.
 
  • #3
CRGreathouse
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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]
 
  • #4
arildno
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And isn't that, really, an expression for sin(x)'s asymptotic behaviour as x ambles peacefully off towards the origin?:wink:

(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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  • #5
CRGreathouse
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arildno said:
And isn't that, really, an expression for sin(x)'s asymptotic behaviour as x ambles peacefully off towards the origin?:wink:

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

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