Quasi-geometric paradoxical division of infinity

[ughaibu]

I was thinking about Aristotle's wheel. I'm not satisfied with the conventional explanation that due to the differing distances between corresponding circumferential points, the smaller (non-drive) wheel is being dragged and slips along it's (the upper) line. In my view, when contemplating the philosophical ramifications of a paradox, appeal to reality constitutes a logical fallacy. Besides, one could lubricate the upper line. In any case, one still has infinite collections of points on both finite circumferences and both finite paths, and one has continuous motion and contact with their respective paths by both wheels. I suggest that rather than pushing the smaller wheel, the extra circumferential distance be used to stretch the upper line. Assuming diameters in a ratio of 2:1, this will give us, in addition to our existing infinite collection of points, an equal infinite collection of non-points on the upper line. But, as the circumference of the wheel, with it's infinite collection of points, is in constant moving contact with the upper line, the infinite collection of points in the upper line must also be continuous. So, the points and non-points need to co-exist continuously throughout the length of our upper line, as such, our resultant is a continuous infinite collection of half-points. Effectively we have a bounded finite half infinity, and by varying the ratio of our diameters, we can divide infinity at will.