Re: The infintely small number b


Since you do not like non symmetric
definitons use

A line L is a set of points.
A segment is a subset of points of the line
whith the form {x in L | a<=x<=b}
[Note by this definition only closed segments
exist. there is no need to consider both
open and closed segments so we ommit open segements
to make things simpler]

Define the process of "cutting" a line at a point
to be the process of forming the subsets A and B.

-pick a point, x
-form two sets, A, the set of points greater than
x and, B, the set of points less than x
-add the point x to A or B.


Joining two segements means taking the union.


Let E and F be subsets of G. It is not
a contradiction to say that the intersection
may not be empty.

When you form a union, a duplicated point in
not included more than once.

- William Hughes
.

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