In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children:
A lie-to-children is a statement that is false, but which nevertheless leads the child’s mind towards a more accurate explanation, one that the child will only be able to appreciate if it has been primed with the lie.
In online discussions about lies to children, most examples I have come across are in the natural sciences, most frequently physics and chemistry. There are some examples on the Wikipedia page as well. Does anyone know of any good examples in mathematics and statistics, particularly at the undergraduate level or higher?
I don’t mean examples where we as teachers simplify and give hand-waving arguments because the level required for a rigorous proof is far too high. What I have in mind are explanations that are completely and utterly incorrect, but somehow still helpful.