[windowojji]

> it's applied to a small enough input

The whole point of big-O notation is to analyze algorithms as they're applied to input of size `n` larger than some `n_0`. Of course it's not useful for small inputs - it's explicitly about large inputs.

> it's implemented very efficiently

On large inputs, it's very hard see how, say, a linear algorithm with a quadratic algorithm regardless of how "efficiently" it's implemented. Assuming you're talking about something like cache friendliness or good register allocation?

[xyzelement]

Yeah we are talking about the same thing. I agree that what you are saying is deeply connected to value of Big O. I am just pointing out that people sometimes forget to consider these things.