Question 7
(NET 1) Given five real numbers $u_0,u_1,u_2,u_3,u_4$, prove that it is always possible to find five real numbers $v_0,v_1,v_2,v_3,v_4$ that satisfy the following conditions:
(i) $u_i-v_i\in\mathbb N$.
(ii) $\sum_{0\le i\lt j\le4}(v_i-v_j)^2\lt 4$.
(i) $u_i-v_i\in\mathbb N$.
(ii) $\sum_{0\le i\lt j\le4}(v_i-v_j)^2\lt 4$.