Please refer the following book for this question: David Hilbert, The Foundations of Geometry, English Translation by E. J. Townsend, Reprint Edition, The Open Court Publishing Company, 1950.
In this book the axiom II. 1 (Page 4) states:
II, 1. If A, B, C are points of a straight line and B lies between A and C, then B lies also between C and A.
My question: In the above statement, what does the words "lies between" mean ? If we take the obvious meaning, then is it not clear that the statements"B lies between A and C" and "B lies between C and A" are same ? Then why should we treat this as an axiom ?