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I'm looking for notation to denote vector substitution and elimination of elements. This is possible using set notation, but I am looking for shorthand notation that is perhaps already in use.

Eliminating the $i$-th element of the vector $\boldsymbol x$ is sometimes denoted by $$ (x_1, \dots, \hat{x}_i, \dots, x_n) = (x_1,\dots,x_{i-1},x_{i+1},\dots,x_n) \stackrel{?}{=} \boldsymbol x_{\hat{i}} $$ My first question: Is the final notation $\boldsymbol x_{\hat{i}}$ commonly used/accepted?

Second, I want to denote substitution of the $i$-th element by some predefined $a$, that is $$ (x_1, \dots, x_{i-1}, a, x_{i+1}, \dots, x_n) $$ What notation if any exists to denote this? E.g. $\boldsymbol x_{i \rightarrow a}$

An existing related question, where the accepted answer suggests notation from game theory: $x_{-i}$ for elimination and $(a,x_{-i})$ for substitution. This question is NOT the same as my question: I'm wondering if a general notation exists to denote substitution, not just elimination, and not just inside the field of game theory.

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    $\begingroup$ Any notation is OK as long as it is defined before it is used. $\endgroup$
    – Alex Degtyarev
    Commented Apr 28, 2016 at 20:06
  • $\begingroup$ @StefanKohl: already addressed in question - see last paragraph. This question does not concern substitution in particular, although the accepted answer gives on example of notation for substitution, which I restated $\endgroup$
    – smörkex
    Commented Apr 28, 2016 at 20:17
  • $\begingroup$ @AlexDegtyarev true, but if notation exists it should not be reinvented $\endgroup$
    – smörkex
    Commented Apr 28, 2016 at 20:18

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