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Order symbol

by Max.Planck
Tags: big-oh, order
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Max.Planck
#1
Nov27-12, 01:26 PM
P: 127
Hi, I noticed in mathematics the O symbol is used in the following way:

A term T is in O(x^p), if lim x->0 T/x^p=c, for a constant c.

While in computer science the O symbol is used is this way:

A term T is in O(x^p), if lim x->∞ T/x^p is a constant.

What gives, these two notations seem to be the complete opposite of each other?
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mathman
#2
Nov27-12, 03:40 PM
Sci Advisor
P: 6,039
The O symbol is valid in both cases. It is up to you to define what the x limit is.
Max.Planck
#3
Nov28-12, 02:18 AM
P: 127
Quote Quote by mathman View Post
The O symbol is valid in both cases. It is up to you to define what the x limit is.
But don't they contradict each other?

For example, in the first case x^7 is in O(x^5), but in the second case it is not.

HallsofIvy
#4
Nov28-12, 07:22 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,353
Order symbol

No, they are just two distinct cases of a general concept. We should aways say "f(x)= O(g(x)) as x-> a and specify a. They are using two different values of a and so getting two different results.
Max.Planck
#5
Nov28-12, 07:57 AM
P: 127
Quote Quote by HallsofIvy View Post
No, they are just two distinct cases of a general concept. We should aways say "f(x)= O(g(x)) as x-> a and specify a. They are using two different values of a and so getting two different results.
Aha, thanks!


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