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Theorem 1.8 Let A,B,X be points on a line having coordinates a,b,x respectively. If $X \notin \overrightarrow{AB}$ and a < b then x < a.

Proof: We assume the A,B,X are points on a line with coordinates a,b,x respectively with a < b and that$ X \notin \overrightarrow{AB} $. We will show that x < a. Assume that x > a. Then by Theorem 4.6, $ X \in \overrightarrow{AB} $. This completes the proof.

I've been looking at this proof and I know something isn't right, but I don't understand what's wrong. Could someone explain?

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    What does $\overrightarrow{AB}$ denote? – 2017-02-14
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    I think a line? – 2017-02-14
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    It most likely denotes some part of the line through $A$ and $B$, but which part? The notation must have been defined in your course, can you look it up? – 2017-02-14

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