I am an economics student and I face the following problem. I want to describe a model with agents with different types which can be described by a tuple $t = (t_1,t_2,t_3)$.
$t_1,t_2,t_3$ can be seen as different characteristics of the agent like the yearly income, education, ethnicity, faith e.t.c
But not all of the characteristics are observable from the outside for example in some instances only $t_1$ and $t_2$ can be observed and in other instances only $t_3$ can be observed.
Therefore I want to assign another tuple to each agent containing the observable characteristics called $t^o$ where $t^o$ can be different for different agents.
My question is whether there is an operator $t O t^o$ such that the result of that operation is a tuple containing only the elements of $t$ that are not in $t^o$.
The analog with sets would be the operation $A\setminus B$. Does such an operation exist for tuples?
Thanks to everybody who takes the time to read this and think about this problem for some time :)
It seems like you need two ideas in the mix: first, an operator which identifies the domain of a partial function (your tuple $t^o$) on the set of all characteristics, and then a restriction or projection operator that restricts the tuple $t$ to the complement of the domain of $t^o$. I don’t know economics jargon, but there might be a way part or all of this is usually formulated in that field.
Ideas from the relational algebra (that founds the theory of database systems and SQL) might be useful, too, as the tuples used there are unordered tuples with values of attributes (which you seem to be dealing with), instead of ordered tuples with positional indexes. I’ve never encountered a single common operator for “project onto the complement of the domain of a partial function” idea, though.