Introduction [can be skipped without loss of generality]. This question was closed and, recently, deleted, perhaps for good reason. It did have an answer with 10 upvotes, and another (mine) with 15 upvotes. So that my answer not be lost to m.se, I pose here a version of the deleted question, and my answer.
Question: Is there any situation in Mathematics where there is a sense in which zero and infinity are identified?
Note: although I am posting my own answer, I would encourage others to post theirs as well.