The first day of first - semester calculus I like to talk about driving to Santa Fe. Distance from Albuquerque is a function of time. Speed is another function of time. But the students swallow that. They understand a graph with a time axis.
Time is a function of distance.
We sweat over them. But we don't acknowledge the complication caused by plain English. This may partly explain why students want to approach a limit only from one side, not in alternating fashion. In practical computation, an algorithm converges when it settles down to one value and stays there - stays till whoever's doing the calculation is satisfied. In advanced mathematics, there's more linguistic confusion.