In the following question please justify each algebraic step you make by referring to the axioms of ordered fields, or one of the theorems stated in §3 of the textbook. You may use theorems stated in the textbook even when the book does not give the proof. Suppose that F is an ordered field, and that a, b, c ∈ F, with c > 0. Prove that the following are equivalent:
1. |a − b| < c
2. a − c < b < a + c
Hint: You will want to use O4, but it is only stated for ≤, not for <, so you will probably want to start by proving a version of O4 for <.