I flagged this post as primarily opinion based. It was declined. I think this decision is incorrect and would like it adjudicated if that is possible. If there is no facility to dispute declined flags, we should consider adding it.
My reasoning is as follows. The OP wants an example of how to show that $0 \times \infty$ product limits are wrong without having to point out that the $\infty$ part is self-evidently wrong. He does not believe this to be the case because, quote: "students just think that because 0 times anything is 0 the answer is 0. And they happen to be right". Which is of course total nonsense, and this is exactly the sort of mistake that should be taught by the OP. His dispute is primarily opinion based, given that it has no logical basis, and so I believe my flag is appropriate. If you read the thread so far, he seems impervious to any reasoning counter to his belief.
If you agree that this flag should have been declined, I would very much like to know why you think the OP's reasoning is appropriate, because I do not. Thanks in advance for your help.