Subject: Re: Dimensions of a line
Date: Wed, 9 Sep 1998 16:23:44 +0100
From: Colin Everest
The point is that my Maths teachers told me that a line was a set of points - it is a particular subset of all the points on a plane. Now that I'm a maths teacher of sorts myself I find myself wondering if what I am passing on can really be true.
Just to say that this is a wonderful mystery doesn't really satisfy me. I can understand how a collection of people can become a society even though people and societies are quite different entities. I would like to be able to explain, similarly, how a collection of points can become a line extended in space even though points and lines are very different entities.
It seems to me that if this can't be done then there is something very wrong with the usually accepted definition of a point as a location without any dimensions or extension in space or with the definition of a line as a set of points. If as I suspect, it is the latter which is wrong,then how can you define a line in a non-circular way i.e. that amounts to more than saying a line is a line is a line....
By the way, I think your site is great. Keep it up and expect many more more visits from me and my students.