I have a question on postulates of the General Relativity (GR). I happened to read from a high school level book (Kerr, Kerr & Ruth 1999, 621) that the postulates of GR are:
1) Mach's principle -Inertial and gravitational forces are indistinguishable.
2) Four dimensional space-time is curved as a result of the presence of mass.
3) Objects take the shortest path between two points in space-time.
Are these postulates correctly stated? Is it really so that GR follows from these three postulates?
I have wondered what is the difference between postulates in physics and axioms in mathematics. Any opinions?