This is an important measure. Let us define it, and then illustrate it's importance. Define:
We can easily show that . So, in a sense is a minimal measure. More often that not, in a practical circumstance, we use as if we are really talking about . It is rare that someone would say that is in a practical sense, although technically, it is in fact true.
One would argue, that from a purely mathematical and logical perspective, we should only use the measure. With a little extra work, we can easily construct the complexity classes from this, rather than naturally letting the classes follow by the use of the Big-O measure. But more about that to follow.