Can someone help me understand the notation used here? I can't seem to figure out the meaning behind what comes after the "if condition".

If Adeline chooses $T$ \begin{equation} U_i=v\min\{e_i,e_j\}-e_i, \end{equation} where $i,j\in \{a,b\}$ but $j\neq i^2$ and $\min\{e_i,e_j\}=e_i(e_j)$ if $e_i\leq (>)e_j$.

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    $\begingroup$ Please do not use pictures for critical portions of your post. Pictures may not be legible, cannot be searched and are not view-able to some, such as those who use screen readers. $\endgroup$ Mar 19 at 14:58
  • $\begingroup$ Hi! I think more context would be helpful to understand the notation. But from what I can recognize: $U_i$ would be $v$ times the value that is smaller between $e_i,e_j$ and then subtracted $e_i$. So, for example, if $e_i$ was smaller, then $U_i=(v-1)e_i$. $\endgroup$
    – P3p3O
    Mar 19 at 15:46
  • $\begingroup$ Then $i,j\in\{a,b\}$ would indicate the possible values $i$ and $j$ can take, subject to the condition $j\neq i^2$. I don't know how $a,b$ are defined or if they can be any number, but if $i,j\in\{2,4\}$ and $i=2$, then $j=2=i$ so that $j\neq i^2$. The last part is confusing since the parenthesis usually indicate multiplication, but, in the way this is written, I think they indicate cases. $\endgroup$
    – P3p3O
    Mar 19 at 15:51
  • $\begingroup$ So, more explicitly, the last part should be written: $\min\{e_i,e_j\}=e_i$ if $e_i\leq e_j$ or $\min\{e_i,e_j\}=e_j$ if $e_i > e_j$. $\endgroup$
    – P3p3O
    Mar 19 at 15:54


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