Question 23
Let $S$ be a given set of real numbers such that:
i) $1 \in S$,
ii) for any $a, b \in S$ (not necessarily different), $a-b \in S$,
iii) for $a \in S$, $a \neq 0$, $\frac{1}{a} \in S$.
Prove that for any $a, b \in S$ we have $a b \in S$.
i) $1 \in S$,
ii) for any $a, b \in S$ (not necessarily different), $a-b \in S$,
iii) for $a \in S$, $a \neq 0$, $\frac{1}{a} \in S$.
Prove that for any $a, b \in S$ we have $a b \in S$.