Which of the words in "absolutely no utility" did you not understand, or was it the three of them together as a phrase that escaped your comprehension?
Let us look again at this complexity:
Code:
{} = ___
{{}} = __|__
|_
{{{}}} = __|__
|_|_
{{{{}}}} = __|__
|_ |_|_
{ {}, {{}}, {{{}}} } = __|____|_____|____
1) If we ignore the complexity of each member then |{ {}, {{}}, {{{}}} }| = 3
2) If we do not ignore the complexity of each member then |{ {}, {{}}, {{{}}} }| = 6
Since your utility is strictly limited to (1) , then (2) has no utility under (1) limitations.
(1) limitation can't measure the existence of complexity because it is tuned to ignore the inner stricture of each member, and as a result, cardinality is the measurement of existence of different members, which cannot avoid the internal structure of each member in order to consider its existence (as a black-box) as a considered element the influences the value of some cardinality.
(1) only approach is an appropriate utility for certain purposes, but from a wider view of the existence of the measured things, this utility is a partial case of (2), and enables us to choose any degree of complexity we wish to choose between (1) and (2) (where (1) and (2) may be included or not) for some utility.
The current standard (1) approach about Cardinality must not be taken a universal principle of Complexity, since it is clearly a partial case of the measured things that avoids the existing internal complexity of each existing thing (which its existence is taken only as a black-box).
