Math is just a tool, as long as the objects behave in the ways you need you can do whatever you want with math.
If your math objects breaks other properties of math that you don't use then it doesn't matter, you don't use those so your math is still correct.
A programmer analogy would be that you implement a special kind of list for your project, but don't implement the whole list interface because you don't need the rest. That makes the mathematicians fume, "it isn't a list!!!", and they invent a new interface name for your implementation, like "distribution" instead of function.
If your math objects breaks other properties of math that you don't use then it doesn't matter, you don't use those so your math is still correct.
A programmer analogy would be that you implement a special kind of list for your project, but don't implement the whole list interface because you don't need the rest. That makes the mathematicians fume, "it isn't a list!!!", and they invent a new interface name for your implementation, like "distribution" instead of function.