A set is only a framework to explore our ideas.

The concept of an oredered set does not depend on the quantity concept as shown here:

By Complementary Logic multiplication is noncommutative,
but another interesting result is the fact that multiplication
and addition are complementary opreations that can be ordered
by different internal symmetrical degrees where the quantity
remains unchanged, for example:

A Number is anything that exists between ({},{__})

Or in more formal definition:

({},{__}):={x|{} <-- x(={.}) AND x(={._.}) --> {__}}

Where -->(or <--) is ASPIRATING(= approaching, but cannot become closer to).

Let redundancy be: more then one copy of the same entity can be found.

Let uncertainty be: more than one unique identity of the same entity can be found.

If x=4 then number 4 example is:

Number 4 is a fading transition between multiplication 1*4 and
addition ((((+1)+1)+1)+1) ,and vice versa.

This fading transition can be represented as:

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