I have a $Set$ of elements $n$ (a multiset).
Each element of this set $n$ is the same, is a multiset because one element $n$ is replicable using addition operation, in other words we can have finitely repeated element set
My problem is just that: I don't want a finitely repeated element $Set$ but just return to a single element $n$ without this being repeatable
The natural numbers are "closed" under addition and multiplication. A $Set$ is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set.
My goal is to find a way to represent a particular natural number X without use the addition because my goal is to avoid to reach this natural number $X$ 'splitting' it into many parts (I don't want a subset as a sum $n+n+n+n+n$..)
But problem is that each element of this $Set$ is a natural number
I perform a sum $n+n+n+n$... until I reach final natural $X$
We have a natural number of addition operations not a 'a natural number' of elements because in my situation $Set$ is a natural number of operations not of elements (that are'numbers')
$X$ = addition$+$addition$+$addition$+$addition...
is not an addition of elements but an addition of addition
$X = n+n+n+n...$
but my problem is this: can we use another category where $n+n+n$.. does not return me a addition of addition but a single element without to form a finitely repeated element set but only 'the element' ?