Example: P = {2, 15, 6, 1, 9, 4, 6, 11, 17, 2, 21, 9}
Say, Q is the set of highest two values of P
Q = {17, 21}
There is no "ready made" answer to your question. sup(P)U[sup(P\sup(P))] would be correct and equal to Q.
There is no "ready made" answer to your question. sup(P)U[sup(P\sup(P))] would be correct and equal to Q.
I agree, to my knowledge there is not a formal definition for that. Maybe you could try to do an inductive definition like this:
Let A a set of N elements {A1, ..., AN}. So, you could define C the set of the highest m values of A (m
If you accept the sort-function (which brings an array of numbers in ordered form) as a mathematical expression, then the solution is obvious: sort to decreasing order, eliminate doubly occuring items, take the first two items. Of course there are much more efficient ways to program this selection. That a traditionally educated mathematician will probably not accept such a program code as 'a mathematical expression' has only historical reasons. Actually all constructs of imperative programming languages are mathematical expressions.
Define sort {A1, A2, A3, ............, An} = { B1, B2, ........ , Bn : Bi >= Bi+1, i=1, n-1}
Then sort-k { A1, A2, A3, ........., An} = {B1, B2, B3, ....., Bk}
In set theoretic notation, you do not know which is bigger of the two.
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