Commonality and Equality

In Common Factor and Common Multiple, "common" is equivocal.  In the former, it signifies some characteristic internal to each element in a set, in the latter, something that encompasses them.  The terms 'Atomist' and 'Wholist', respectively, can be used to distinguish the two types of Commonality. Thus, for example, in the expression 'common ground', and its usage in the preamble to the U. S. Constitution, Commonality is Wholistic.  In contrast, when a quantity is a property of each element of a set, its Commonality is Atomist.  In other words, Equality is Atomist Commonality, which suggests that its relation to the Constitution is problematic.