Landau Notation and Local Comparison of Functions - The little o.
Yeah, this one sucks.
You may also have heard of this as the "Little-O/Big-O" or "Theta-Omega" notation.
As you may have seen on the lecture 10 file, on the definition, we first defined two functions
But why this "neighbourhood"? Because we need limits.
The limit is as a function tends to a point, and, you know, to approach a point, the function needs to be defined around it. That's why we need a neighbourhood. Because we'll use limits.
This may seem a bit confusing, but it's just so you can understand what we mean when we say, for example, that
Let's take these two functions as an example:
The function
It will be so large that, you know, if we compare to it, x is practically nothing:
And for the final infinity stone ha, ha, based on the above info, calculate this limit:
You may still be a bit confused, but that's okay. You'll get it now.
Understanding The Little o