The mathematical notation for a subset with given conditions

Question

Assuming I have a set $A$ of numbers, I'd like to mathematically notate a subset $B$, such that the cardinality of this subset is $x$ and its elements are the greatest $x$ elements of $A$. So, how can I mathematically notate this? Thank you very much for any help.

Answer 1

One attempt:

Assuming $A$ has a maximal element, we can define a function to determine the set without the maximal element: $$ f(A) = A \setminus \{ \max A \} $$ Then $$ f^{x}(A) = (\underbrace{f \circ \dotsc \circ f}_{x})(A) $$ is $A$ without the $x$ largest elements. Note: we did not provide any fail-safe that $A$ has $x$ largests elements.

Then $$ B = A \setminus f^{x}(A) $$

Another attempt: $$ f(A, y) = (A \setminus \{ \max A \}, \max A) \\ B = \bigcup_{k=1}^x \pi_2(f^k(A, \cdot)) $$ where $$ \pi_2(x, y) = y $$ is the projection for the second argument and $\cdot$ stands for whatever value (it is ignored anyway).