You guys are rehashing the basic dilemma of Zeno's paradox and the only thing that is absolutely certain is that you will never resolve the infinities of multiplication and division with any notion of space. The real number line is a construct of human consciousness that effectively and pragmatically deals with infinities. Space is a construct of human consciousness that effectively and pragmatically deals with the lonely nothing of amaterial inaction.
The association of the real number line with spatial displacements is therefore no accident. We keep track of action over time largely by imagining objects on trajectories that are displacements in space. However, all action simply involves changes in object mass and phase and exchanges of matter between objects with certain coherence. We deduce displacements in space by changes in mass and their phases and do not even realize it.
Space is just a convenient representation of consciousness that expresses the duration and phase of time between object actions. The infinities of multiplication as well as the infinities of division are both rooted in the way that we imagine space. In other words, we imagine space just like we imagine the real number line. They are convenient tools of consciousness that allow us to effectively predict action.