Basic Analysis I — Real Analysis · Problem 1.1.8

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · fields

Problem

Let

F := \{0, 1, 2\}

. a) Prove that there is exactly one way to define addition and multiplication so that

F

is a field if

0

and

1

have their usual meaning of (A4) and (M4). b) Show that

F

cannot be an ordered field.