Real numbers/Ordering axioms/Archimedean/Implications/Fact/Proof2
Proof
(1). We consider . Because of the Archimedean axiom there exists some natural number with . Since is positive, due to fact also holds. For (2) and (3) see exercise.
(1). We consider . Because of the
Archimedean axiom
there exists some natural number
with
.
Since
is positive, due to
fact
also
holds. For (2) and (3) see
exercise.