Symmetry:

Let x be a general notation for a singleton.

When a finite collection of singletons has the same level, it means that all singletons are identical, or have the maximum symmetrical-degree.

When each singleton has its own unique level, it means that each singleton in the finite collection is unique, or the collection has the minimum symmetrical-degree.

Multiplication can be operated only among identical singletons, where addition is operated among unique singletons.

Each natural number is used as some given quantity, where in this given quantity we can order several different sets, that have the same quantity of singletons, but they are different by their symmetrical degrees.

In a more formal way, within the same quantity we can define all possible degrees, which exist between a multiset and a "normal" set, where the complete multiset and the complete "normal" set are included too.

As this example of transformations between multisets and "normal" sets shows, the internal structure of n+1 > 1 ordered forms, constructed by using all previous n >= 1 forms:

1
(+1).=.{x}

2
(1*2)......=.{x,x}
((+1)+1).=.{{x},x}

3
(1*3).............=.{x,x,x}
((1*2)+1)…...=.{{x,x},x}
(((+1)+1)+1).=.{{{x},x},x}

4
(1*4)........................=.{x,x,x,x}.<---------- Maximum symmetrical-degree,
((1*2)+1*2).............=.{{x,x},x,x}.............Minimum information's
(((+1)+1)+1*2)........=.{{{x},x},x,x}..........clarity-degree
((1*2)+(1*2))...........=.{{x,x},{x,x}}.........(no uniqueness)
(((+1)+1)+(1*2))…..=.{{{x},x},{x,x}}
(((+1)+1)+((+1)+1)).=.{{{x},x},{{x},x}}
((1*3)+1).................=.{{x,x,x},x}
(((1*2)+1)+1)..........=.{{{x,x},x},x}
((((+1)+1)+1)+1).....=.{{{{x},x},x},x}.<---- Minimum symmetrical-degree,
.......................................................................Maximum information's
5.....................................................................clarity-degree
... ...................................................................(uniqueness)