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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 $x_j \ge y \ge x_{j+1}$

thanks in advance

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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.

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  • $\begingroup$ does that notation make it clear that the $x_j$ are ordered? $\endgroup$ – phdmba7of12 Oct 30 '20 at 16:09
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    $\begingroup$ No, I assumed that was stated beforehand. $\endgroup$ – Jair Taylor Oct 30 '20 at 16:10
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    $\begingroup$ (to be clear, the use of $j^*$ is not a special notation that implies anything - you can call that variable whatever you like.) $\endgroup$ – Jair Taylor Oct 30 '20 at 16:11

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