humphreys wrote:I think all of these issues regards infinity are solved if we accept that there becomes a point in nature where you cannot divide by two anymore, something like the plank constant.
Either that or mathematics itself is insufficient to deal with the issue perfectly. The distance between two points cannot actually be infinite, even if mathematics might suggest it is, otherwise motion would be impossible.
I'm sure I do not know enough about math to have this issue correct concerning infinity, potential or actual, countable and uncountable as I've seen defined looking some of it up.
It does show, and we have all pointed out some areas of Math that result in some of these things. The concept of any measurement depends on to what increments you want to express it. The size of the desk, or distance between our homes is countable but only in sensable increments, that are also usable. Obviiously the smallest increments to measure with would be how many atoms wide is it? You would next ask, what atom, they are all different too? If I got in the car to head over for Thanksgiving dinner and asked, "How may atoms is it"? I doubt if we have a number with that many digits. It isn't countable, but it is countable in miles, or blocks, or minutes of driving. Again, it gets back to agreed upon rules of Mathematics (
) that we have a concenceous about, and agreed upon increments or rounding. Math is an approximation, with a tolerance + or -.