So I have a matrix $A=[a_{ij}]_{\forall\,i,j\in\{1,\dots,n\}}$.
I have no problem to define a set $S$ as $S:=\{j: j=\text{argmax}_{j'}\; a_{ij'},\forall i\in\{1,\dots,n\} \}$ for example. In fact, I have seen sets defined this way many times.
Now my problem is with tuple. Is it correct to use the same for tuple. So, can I say "let $A$ be the tuple $A:=(j: j=\text{argmax}_{j'}\; a_{ij'},\forall i\in\{1,\dots,n\} )$." or this makes no sense?
EDIT
In fact, I have a bad time finding some mathematical object that is like array in programming language. So I can access elements of that object, find its size, add elements, remove elements, etc. Is there any mathematical object like this?
Best Answer
I would just write the tuple out to avoid any confusion or ambiguity with the order:
$$x = (x_1,\ldots,x_n),\ x_i = \operatorname{argmax}_j a_{ij}$$
Edit: Mathematical objects don't need to be "implemented". Just write what you want your reader to understand. To add an element $y$ to $x = (x_1,\ldots,x_n)$, just write "$x' = (x_1,\ldots,y,\ldots,x_n)$ where $y$ is inserted in the $i$-th position". To define its size, write "Let $n$ be the length of $x$.". To remove an element, write $(x_1,\ldots,x_{i-1},x_{i+1},...,x_n)$.