(April 28, 2016 at 9:04 am)robvalue Wrote: As for whether a finite object being represented by an infinite number of subsections is "real", I'm not really sure how to answer it. A line is a continuum anyway, and consists of an infinite number of points along the way. So you move through infinitely many iterations to move a finite distance. This is just a different way of "counting" the distance, rather than adding it continuously. So yes, I'd say it's a logically possible way of viewing an object. Obviously it doesn't become split up into all this bits just because it's possible; but it still is the sum of all those bits. If you removed any, you'd no longer have the whole length.
I have been thinking about this saying that "a line is made up of an infinite number of points" lately. The point doesn't seem to be very well defined. It seems that to me, that the only way you could get an infinite number of points, is if you have your point defined with zero size or length. In which case, if you add them, you are not going to get anywhere. Any number greater than zero, will get you to the overall length, but in a finite number of steps. The same with dividing the line. It is potentially infinite provided, that you can keep dividing into smaller segments. But, at each step, it is still finite. You are talking about an unending process which is potentially infinite but finite at each point.
There is also the law of non-contradiction, which states that contradictory statements cannot be both true in the same way, at the same time. A line cannot be both finite in length and infinite. Therefore, in order for the statement that it is made up of an infinite number of points, the definition of points cannot be related to length. If this is the case, then wouldn't it be incorrect to make a correspondence between the points and the length afterwards?
