Ah, I was starting with bounded objects on purpose to build intuition, but I tried to be clear in my language about when I was talking about bounded vs unbounded objects. I was aware that the question was about unbounded objects. I thought it would be easier this way because it's hard to visualize intersecting 3D spaces correctly, so I wanted to show that picturing them as bounded volumes leads to the wrong conclusion by way of analogy to lower dimensional objects. I left out the null intersection case for brevity.

Thanks for the more thorough explanation!