What are some conceptualizations that work in mathematics but are not strictly true? I'm having an argument with someone who thinks it's never justified to teach something that's not strictly correct. I disagree: often, the pedagogically most efficient way to make progress is to iteratively learn and unlearn along the way. 

I'm looking for examples in mathematics (and possibly physics) where students are commonly taught something that's not strictly true, but works, at least in some restricted manner, and is a good way to understand a concept until one gets to a more advanced stage.
How about this notorious one I remember from high school?

"$f(x)$ is just a fancy name for $y$."
The existence of Gabriel's Horn.


  That is, there exists an object with a finite volume but with an infinite surface area.


Mathematically, we can show this to be true by taking a 360-degree revolution of the graph $y=\frac{1}{x}$ in the domain $[1,\infty)$ about the $x$-axis, and calculating its volume ($\pi$) and its surface area (infinite).

This is all well and good in theory, but in our physical world, no such object exists.

One of the reasons for this is that the thickness of the horn is limited by the size of the atom, so cannot be arbitrarily small.