Suppose I have 4 real numbers in $[0,1]$, all different between each other.
Assume that there exists a way of ordering the four numbers such that: $$ \begin{cases} w_1>w_2\\ w_3=1-w_1\\ w_4=1-w_2 \end{cases} $$ where $w_1$ is the first number in the ordered sequence, $w_2$ is the second number in the ordered sequence, $w_3$ is the third number in the ordered sequence, $w_4$ is the fourth number in the ordered sequence.
Is such a way of ordering unique? If yes, could you sketch the proof? In not, could you give a counterexample?