Let there be a set C of discrete values, and a function f be defined for all values belonging to C. Say we define the dependent variable t as:
t = xₖ such that f(xₖ) is maximum among all values of f(xᵢ) where xᵢ belongs to set C.
which may also be written as:
t = xₖ : f(xₖ) is maximum among all values of xᵢ, xᵢ∈C
I am looking for a symbol to represent "among all values of" in the above context. Note that the for all values of (∀) symbol does not suffice.
Something like this should do:
$$t = \underset{x_k\in C}{\mathrm{argmax}}f(x_k)$$
For something more general, maybe you can use the $\forall$ symbol by saying something like $t = x_k : \forall x_i, f(x_k) \geq f(x_i)$