
Re: Several Question Experiments
Posted:
Nov 19, 2013 5:38 PM


On Saturday, November 16, 2013 4:09:40 PM UTC8, Barry Schwarz wrote: > On Sat, 16 Nov 2013 14:06:55 0800 (PST), David Elkins > > <davidelkins777@gmail.com> wrote: > > > > >Question Experiment 1: > > > > > >Imagine a line infinitely long in both directions. Take a pair of scissors, cut it and push the two sections apart one foot. Insert a foot long line. Is the line now one foot longer than infinity? > > > > Draw line segment 1 from (0,0) to (2,0). > > Draw line segment 2 from (0,1) to (1,1). > > > > Drop any number of vertical line segments from segment 2 down to > > segment 1. Each point on segment 2 has a corresponding point on > > segment; they both have the same x coordinate. No point past (1,0) on > > segment 1 corresponds to any point on segment 2. So segment 1 has > > more points than segment 2. > > > > From point (0,2), draw any number of line segments to points on > > segment 1. Each drawn segment passes through segment 2. Each point > > on segment 1 has a corresponding point on segment 2 and each point on > > segment 2 has a corresponding point of segment 1; the segment 1 x > > coordinate is twice the value of the segment 1 x coordinate. So > > segment 1 and segment 2 have the same number of points. > > > > Once you understand how both conclusions can be correct, you will have > > the answer to your query. > > > > <snip> > > > > >My name is David Elkins. I came up with these two questions and would like to know what people think of them. > > > > The first has been a standard discussion item in mathematics courses > > for at least 6 decades and probably very much longer. > > > >  > > Remove del for email
Hello, I posted the initial thread. I have been unable to get to the Google groups for the last few days. I will take the next day or so looking at the various responses. I will do my best to get a 'content' reply to each. Sorry about the delay. Thank you, David,

