2.7.5(1) Let R1 and R, be ordered fields that satisfy the Least Upper Bound Property, and let p: R1 for all x, y E R1. (1) Prove that p(0) = 0 → R2 be a function. Suppose that p(x + y) = p(x) +p(y)

2.7.5(1)

Please include a formal proof.

Extracted text: 2.7.5(1) Let R1 and R, be ordered fields that satisfy the Least Upper Bound Property, and let p: R1 for all x, y E R1. (1) Prove that p(0) = 0 → R2 be a function. Suppose that p(x + y) = p(x) +p(y)