# Order symbol

by Max.Planck
Tags: big-oh, order
 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?
 Sci Advisor P: 5,776 The O symbol is valid in both cases. It is up to you to define what the x limit is.
P: 127
 Quote by mathman 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.

PF Patron
Thanks
Emeritus
P: 38,429

## 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.
P: 127
 Quote by HallsofIvy 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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