Opposites Attract: Understanding O Notation in Math & CS

[Max.Planck]

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?

 

[mathman]

The O symbol is valid in both cases. It is up to you to define what the x limit is.

 

[Max.Planck]

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]

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]

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!