Lebl-Basic-Analysis-I · Problem 1.1.8

Real Numbers

Mathematics · ordered-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.