I've heard several times that for sufficiently small values of n, O(n) can be thought about/treated as if it's O(1).

Example:

The motivation for doing so is based on the incorrect idea that O(1) is always better than O(lg n), is always better than O(n). The asymptotic order of an operation is only relevant if under realistic conditions the size of the problem actually becomes large. If n stays small then every problem is O(1)!

What is sufficiently small? 10? 100? 1,000? At what point do you say "we can't treat this like a free operation anymore"? Is there a rule of thumb?

This seems like it could be domain- or case-specific, but are there any general rules of thumb about how to think about this?

I've heard several times that for sufficiently small values of n, O(n) can be thought about/treated as if it's O(1).

Example:

The motivation for doing so is based on the incorrect idea that O(1) is always better than O(lg n), is always better than O(n). The asymptotic order of an operation is only relevant if under realistic conditions the size of the problem actually becomes large. If n stays small then every problem is O(1)!

What is sufficiently small? 10? 100? 1,000? At what point do you say "we can't treat this like a free operation anymore"? Is there a rule of thumb?

This seems like it could be domain- or case-specific, but are there any general rules of thumb about how to think about this?