when does something belong? when is something included? say we have a set g containing three elements. these three elements are said to belong to g; they have been counted by the set — i.e., counted , presented , structured , situated . it is this situation to which they owe their *consistency*. one wonders: what do we owe to the situation that counts us? to that which we belong? to that which maintains our *consistency*? or, what does that situation owe to us? what if the name of this situation is “pony”?

a set’s subsets are not said to belong to that set. instead, we say they are included. for our set g of three elements, eight subsets are possible. (you might check our pictorial rigor above.) the empty or null set, { }, is trivially included in every set, so we count it as a subset of g. the set which actually does the counting of the subsets of g is called the power set, p(g).

so, why make such a fuss about this rather simple distinction between belonging and inclusion? let’s first cast the issue in slightly different, yet familiar, terms: together, this pair draws out the fundamental distinction between what is mere presentation and the (immeasurable) excess of representation — where presentation stands for the originary count of a set’s elements (a count of belonging), and representation stands for the power set’s count of a set’s subsets (a count of inclusion).