Date: Jan 28, 2014 1:49 PM
Author: Joe Niederberger
Subject: Re: A question about straight lines
>though they may have been thinking ?physical?.
Yes, its my inference. Either "Neighbor" is speaking naively, in which physical and mathematical notions are often confused, or he is purposely doing so, to make some point that is not clear.
For example, Neighbor says:
If there is an infinite number of points on them and each point is dimensionless (i.e. nothing, having neither breadth nor width) then the sum of infinite points which are nothing will have as sum also nothing, but if we admit that a point has only breadth (a very small amount but not 0), then the sum of infinite points will also have breadth, and since they are infinite the straight-line they made up is also with infinite breadth (i.e. an infinite straight-line).
I think its clear he is drawing on physical intuition here at least partially, and its either because he doesn't know how the real number system is treated formally or he intentionally doesn't care.