Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$? I was on the tube and overheard a dad questioning his kids about maths.  The children were probably about 11 or 12 years old. 
After several more mundane questions he asked his daughter what $1/0$ evaluated to. She stated that it had no answer. He asked who told her that and she said her teacher. He then stated that her teacher had "taught it wrong" and it was actually $∞$.
I thought the Dad's statement was a little irresponsible.  Does that seem like reasonable attitude? I suppose this question is partly about morality.

This has been treated extensively both in this question and in others. But I think the clearest formulation possible is this : for me the most correct answer is "NaN", Not a Number.
It is not wrong to say that $1/0 = \infty$ from a topological point of view (be it an Alexandrov compactification, or a projective space), and it's actually very useful and natural in some contexts.
However, as pointed out by everyone, it cannot be made coherent with arithmetic laws, addition and multiplication. So it's "not a number".
That said, for pedagogical purposes I think it's best to not go into these things and just illustrate the arithmetic problems arising when defining division by 0 (and maybe say something like "one might define 1/0 in some contexts, but we will not because of these problems"). Indeed arithmetic notions are much more intuitive than abstract, topological constructions at this stage. 
