The proof of (5) only goes through for n∈N.
You can prove a version of (8) from (5), namely, f(b)=1⇒f(bq)=q for q∈Q, but this doesn't pin down f completely, unless you include a continuity condition.
by Kaya Fallenstein Jun 29 2016
The proof of (5) only goes through for n∈N.
You can prove a version of (8) from (5), namely, f(b)=1⇒f(bq)=q for q∈Q, but this doesn't pin down f completely, unless you include a continuity condition.