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I was wondering if there is a formal way to say that "x is the i-th greatest element in a subset of $[n]$" (or maybe is this formal?).

For example if i have $M=\{2,3,5,7,11,20\}$, how can I say that if I take 7, this is the 3rd greatest element in $M$. And in general, if I want to refer to some arbitrary x, how should I say this?

What iI am actually doing is trying to build a function that takes the i-th greatest element of a subset of $[n]$ to some value, but I want to make it as formal as possible when referring to that element.

Thanks.

Mangostino
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    This is related to “order statistics.” On the Wikipedia page for that, given $M={X_1,\dots,X_n}$ of a set, they use $X_{(i)}$ for the $i$th largest number. But that notation comes from probability, it is not, as far as I know, common outside of probability and statistics. – Thomas Andrews Oct 04 '21 at 18:01
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    @ThomasAndrews That notation is for the $i$th smallest number. – RobPratt Oct 04 '21 at 20:49
  • Potato-Potahto. :) @RobPratt – Thomas Andrews Oct 04 '21 at 21:39
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    One suggestion could be: Given $M$, let $m_1,\dots,m_{|M|} \in \mathbb{N}$ with $m_1>m_2>\dots>m_{|M|}$ be such that $M = {m_1,\dots,m_{|M|}} $. Then $m_i$ is the $i$-th greatest element of $M$. Or maybe a little less formal: Let $m_1,\dots,m_{|M|} \in \mathbb{N}$ be the elements of $M$, ordered descendingly. – Andreas Lenz Oct 04 '21 at 21:58

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