(March 5, 2018 at 1:08 pm)RoadRunner79 Wrote:(March 5, 2018 at 12:52 pm)polymath257 Wrote: OK, then what do *you* call it when something doesn't correspond in quantity to a counting number?
1.) The counting numbers do not 'end' if ordered in the usual way. But, for example, the *negative* counting numbers *do* have an 'end' when ordered int he usual way. The question of 'having an end' depends on the *order*, not on the quantity.
2.) No, those locations correspond to points on the physical line. And yes, they are an *actual* infinity of points.
1.) Ok... if all positive integers end in one direction, and all negative integers end in one direction. Would you agree, that they are infinite in at least one direction. This would be a definition of a ray. Now are you telling me, that when definitions say that the ray proceeds infinitely in one direction, that this is telling me something about the order, not that the line goes on without end?
2.) So the points correspond to locations, and the locations correspond to points. My question is what does a point or a location or a point like under a microscope?
1) Both are infinite. Yes, having an 'end' is a matter of how things are ordered, NOT a matter of the quantity.
The interval from 0 to 1 has an infinite number of real numbers, but has an end at both ends.
2. ???? What does time look like under a microscope? Silly question.