[see also: aim, purpose
At the end of Section 2, we prove...... [Not: “In the end of”]
Now F is defined to make G and H match up at the left end of I.
We shall find it convenient not to distinguish between two such sequences which differ only by a string of zeros at the end.
To this end, we first consider...... [= For this purpose; not: “To this aim”]
Thus in the end F will be homogeneous. [= finally]
[see also: conclude, finish, terminate] The path ends at x.
The word ends in a.
a word starting with a and ending with b
The exact sequence ends on the right with H(X).
We end this section by stating without proof an analogue of......