Re: Hilbert's Geometry Axioms

Is it possible to define "line" using the notion of between-ness,
rather than leave "line" as undefined?


I wish I could remember the title of the book I used many years ago at
Texas A&M. In that approach a "geometry" consisted of points, lines
and planes, with the requirement that if two different lines
intersected they did so in a point, and likewise if two different
planes intersected they did so in a line.

The simplest "geometry" is the four vertices of a trinagular pyramid.
The individual vertices are "points", the lines are pairs of points and
the planes are any three points. At this stage there is no "between",
but the course went on, adding concepts as it needed, proving SAS etc
from basics. Fun book.

.

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