# Tag Info

Following up on my comment on the original question, I have finally managed to construct a counter example that shows that the statement is not in fact correct. Define the positive part of a function, $$[x]^+ = \begin{cases}x & \text{if x\ge 0} \\ 0 & \text{otherwise.}\end{cases}$$ The let  \sigma_1(y) = 1+ \left[\tfrac 14 - |y-1|\right]^+ \$...