do you recall the defintion of a limit? we can say that the function is decreasing and is bounded, which means that there is some g(x) that the value of the function cannot attain, because it is at the boundary. thus we can say that as x is going to infinity, our distance between each g(x) and the boundary is getting arbitrary close. and of course, we can say this more formally (using the definition of a limit) to show that a limit exists and is in fact the boundary