[see also: aim, end, object, objective, intention
Let us now take a quick look at the class N, with the purpose of determining how much of Theorems 1 and 2 is true here.
For this purpose, we first define......
The purpose of this paper is to provide simple exact upper bounds for the case where......
A detailed exposition, more suited to the purposes of the present article, is given in [9].
The motivation for the results of this section is the following result of John (paraphrased slightly to suit our purposes).