Yes, this is a fair point! Interestingly though, projective geometry already provides us with a space potentially suited to this question — I find https://en.m.

Yes, this is a fair point! Interestingly though, projective geometry already provides us with a space potentially suited to this question — I find https://en.m.wikipedia.org/wiki/Projectively_extended_real_line https://en.m.wikipedia.org/wiki/Projectively_extended_real_l... to be a good introduction, although I’m not terribly familiar with the field myself. The intuition behind this choice is, if we’re squishing the rectangle so hard that one side approaches 0 length, the constant area has to go somewhere. If the other side length approaches infinity, why not literally let its measure be infinity? One would argue that the real numbers are too impoverished to give a satisfactorily general answer to our original question. Of course, we still obtain a zero area, so we’re no longer really solving the same problem as we started with. If we want a zero side length and a non-zero area, we may need to move into non-Euclidean geometries. It really depends on what we’re doing. My point is that when an application needs to make changes to the foundation, usually there’s going to be a richer pure setting we can move to. And if there isn’t yet, that’s a great opportunity to find out how robust of a new foundation we can create. Hiding edge cases away in an otherwise unobtrusive definition bothers me as both a mathematician and as a software developer. In all cases, I want to highlight the assumptions we’re making and find the right abstraction to tame them.