I think your math skills and clear understanding of the rules is awesome.
However,... if I were programming an animation and it's following a path y= 2/x, I'm going to have a smooth motion along screen at position 2 until I get to Zero.
So do we handle it as an error? Undefined of course means undefined but do I have my animated plane just blink "undefined" at a random location and then suddenly re-appear on the screen?
In this case, I'd imagine that having the prior two locations and next (estimate) would be handy to determine what y is when x = 0.
Or perhaps we have a built-in exception handler if x = 0 BEFORE we calculate when we have x in a division statement. For instance, if we have a point on the screen and try and follow the mouse, there are 4 points where one of our numbers reaches 0.
Consider this script;
this.rotation = Math.atan2((object.y - mouse.y), (object.x - mouse.x)) * 180 / Math.PI;
These days -- that code will work. Likely because someone at Adobe built in a handler just for these cartesian dilemmas to figure out at which quadrant X and Y were pointing to.
Does it make practical sense that if X = 0, then X = .0000001 will get you a reasonable facsimile of what should occur with X?
That solves the need to test for "undefined" -- even though more programming environments might be robust with regard to divide by zero errors.