REMARKS ON W QUESTION #3


Here are some things I wanted to write on many papers.  Keep in 
mind when doing your revision.

1) Redefining the betweenness relation does not change the 
incidence axioms at all, so it is not necessary to reprove them 
in detail (although they should be mentioned).  If you did state 
or prove them, there's no need to erase them now.  On the other 
hand, B-1 and B-2 do need to be checked in the midpoint 
interpretation.

2) The model we are working on contains ALL points of the 
Euclidean plane, with their standard distances.  So, it should be 
easy to give a counterexample to B-3 without a lot of fuss.  It 
is not necessary to build the counterexample out of the points 
you exhibited to verify B-2.

3) Start out your essay by stating clearly what the model is -- 
in particular, the new definition of "between" and "*".  You 
can't assume that your reader is looking at Greenberg's book.