Question 14
Consider all functions $g:\mathbb R\to\mathbb R$ satisfying the conditions that
(i) $|g(a)-g(b)|\le|a-b|$ for any $a,b\in\mathbb R$;
(ii) $g(g(g(0)))=0$.
Find the largest possible value of $g(0)$.
(i) $|g(a)-g(b)|\le|a-b|$ for any $a,b\in\mathbb R$;
(ii) $g(g(g(0)))=0$.
Find the largest possible value of $g(0)$.