math notation question regarding location within ordered set

if $$\{x_i\}$$ for $$i=1...N$$ are a set of ordered values such that $$x_1\ge x_2 \ge ... \ge x_N$$ how do I notate most efficiently for a given number $$y$$ where $$x_1 \ge y \ge x_N$$ the maximum subscript $$j$$ such that $$x_j \ge y \ge x_{j+1}$$

I would write $$j^* = \max \{j : x_j \geq y \geq x_{j+1}\}.$$ Of course, there's also nothing wrong with the way you defined it in words.
• does that notation make it clear that the $x_j$ are ordered? – phdmba7of12 Oct 30 '20 at 16:09
• (to be clear, the use of $j^*$ is not a special notation that implies anything - you can call that variable whatever you like.) – Jair Taylor Oct 30 '20 at 16:11