Given a set $A$
I would like to know if already exist a math definition for a Set $L$ being:
$L$="the smaller cardinal set from a choice between a set and its complement"
i.e a set with this properties
$L=A$ , if $|A|$ $\lt$ $|\overline A|$
$L=\overline A$ , if $|A|$ $\gt$$|\overline A|$
and $L=A$ or $L=\overline A$ (indistinct when tie) , if $|A|$ = $|\overline A|$
I just wonder if it has any known use or name, perhaps is too trivial to have a name, but that's the question. thanks
$A$ is a subset of a countable set $X$.
UPDATE 2: a comment about this function
As I told before the operation is very simple to have a name, but just for reference, or fun, I would like to share with you a comment about the source, I call it the Law operation to the set A, L(A) (it could be called the legislation function or rule operation, etc..). Why? because in every legislation process there are admissible and inadmissible things, legal and illegal, permitted and prohibited, possible and impossible and so on.. for example in physics there are laws of physics, that include and exclude certain possibilities, the fact is that we never call it laws when the cardinal of excluded things are bigger than the included, because if were so, we would just legislate the complement, i.e. fewer laws to legislate the same. L could be from Leibniz too, because it's his idea that "when a rule is very complex, what is conformable to it is seen as irregular", so I wanted to reduce that concept, to the minimum complexity taking into account only the number of facts that the law regulates.