I think we will leave that point where it is, Steve, or I will have to try to give the mathematics of what an asymptote is, which will strain mudcats ability to display the mathematical symbols required, my patience persuading a limited text based tool to lay things out as I need and everyone else's temper wondering what the hell that bunch of symbols mean. The definition you give, though, misses the essential point of being an asymptote as many other things apart form asymptotes meet your definition.

I take your humility point, at least in the abstract. Like all the rest of the human race, such humility is not always obvious in individual scientists, but yes, a need for humility is certainly built into the sciences.