Given a function F let us say that the useless limit of F at a is L if there is some \delta>0 \text { and some } \begin{aligned} &\epsilon>0 \text

{ such that if } 0<|x-a|<\delta \text { then }|F(x)-L|<\epsilon . \text { If this holds, then denote it by }\\ &\lim _{x \rightarrow a}^{\text {useless }} F(x)=L . \text { Prove that } \lim _{x \rightarrow 0}^{\text {useless }} x=1 / 2 \end{aligned}