I need some help with this proof that i'm not shure i've covered it correctly. It is about the position between points in a line.
The problem follows:
Let A,B,C be points in a straight line and a,b,c their coordinates in that line. When the point B is between A and C, we write A*B*C or C*B*A. It is known that this can only happen if:
$a<b<c$ or $c<b<a$
Now show that if A*B*C and A*C*D, then B*C*D and A*B*D
Here is my approach to this proof:
If A*B*C and A*C*D, then:
$a<b<c$ and $a<c<d$
i. We have $b<c$ and $c<d$ that implies $b<c<d$ $\rightarrow$ B*C*D
ii. We have $a<b$ and $b<d$, that implies $a<b<d$ $\rightarrow$ A*B*D
I need to know if this is sufficient to prove the statement.
Till now you have only shown the interpretation of $A*B*C$. But you are missing one inequality- $c<b<a$.