With a finite amount of points on a line, show that the points can be labelled as B1, B2, B3, ..., Bm so that Bj is between Bi and Bk only if j is between i and k.
How can this be done? I am not sure how to interpret the question.
Proof of Labelling a Line
0
$\begingroup$
geometry
-
0Ummm, draw some points. I don't see the problem here. Also, define "j is between i and k" – 2017-02-13
-
0You'll want to prove this constructively. If you use the real line, what $x$ value could you assign to each $B_i$ to make that come true (hint: don't overthink it :) – 2017-02-13