Axiom talk:Outer Transitivity of Betweenness

The notes state that $b\ne c$ (luckily). It is necessary, for otherwise we would have (taking $b=c$, $a=d$):


 * $\mathsf B abb \land \mathsf B bba \implies \mathsf B aba \implies a = b$

Furthermore, the first two conditions are satisfied by Axiom:Reflexivity of Betweenness. That is, there could only be one point under the assumption that there are lines. This is most undesirable :). --Lord_Farin 08:05, 25 January 2012 (EST)