
Re: A question about straight lines
Posted:
Feb 2, 2014 10:55 PM



I always wanted my students to understand that all conclusion are base on undefined terms, defined terms, basic assumptions, and conclusions from these. Don't tell your students what to think, but teach them how to think! (in everyday situations as well as in Math)
On Sat, Feb 1, 2014 at 12:05 PM, Joe Niederberger <niederberger@comcast.net>wrote:
> R Hansen says: > >If Neighbor understood real numbers and applied that to points, he would > then be able to use what you wrote. He is still struggling with an > incorrect sense of what points are. He still has a tendency (as all of us > do) to think that two points can be beside each other, with no other point > in between. The only way I know of getting over that tendency is to study > the real numbers and what we mean by ?point? and ?line?. > > You don't need to know everything about real numbers to follow my > interpretation, and arrive at an understanding that (1) lines today are > (usually) viewed as sets of points, (2) the cut point has to belong to one > subset or the other but not both, assuming (3) you want exactly two subsets > that are disjoint and when unioned give back the original. > > That much is very elementary, naive, set theory. Sure there's that can be > said, but one step at a time, huh? > You don't need to get into density and limits and whatnot > to look at what's going with the cut point itself. > > I arrived at this by reading Neighbor's questions and trying honestly to > see what he was after. I could be wrong. > > Cheers, > Joe N >
 Jim
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