Basic Analysis I — Real Analysis · Problem 1.1.11

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · ordered-fields

Problem

Let

F

be an ordered field and

x, y, z, w \in F

. a) Prove part (vii) of Proposition 1.1.8. That is, if

x \leq y

and

z \leq w

, then

x + z \leq y + w

. b) Prove that if

x < y

and

z \leq w

, then

x + z < y + w