A set is a collection of elements/members, and the identity of the set is defined by its members, or elements. The identity distributes over its elements/members. For example the set of natural numbers has a type of identity, "natural number". Sets are subsets of larger sets and the larger set has a distributive identity that distributes over its contents.

So the distributive identity forms a relation.

The set of all dogs has the identity of "dogness" and that set is contained by the set of mammals which has the identity of "mammalness".

Finally we reach the highest most inclusive set/container/relation, the "set of all that exists". The "G"[God] identity distributes over the whole shebang.

G[sum of all that exists]

G[a+b+c+...+n] = Ga + Gb + Gc +...+Gn

G[God] is the greatest common factor. Take any two "things" that exist and see what is different and factor out the common elements, and begin to break the common factors down to the most basic ones. Take two pieces of matter, for example, apples and oranges, at a more basic level they are just forms of energy. Take energy and spacetime and discover that they are mutually dependent in a fundamental way, related by a common factor. Keep going until the most basic factor is derived/discovered, G.

From the "G" factor, all possible information about the universe can be derived. Every possible universe that follows from the "G" principle is equivalent to an infinite amount of information. Therefore God is omniscient.

From the first principle, the "G" factor, everything exists, since it is the greatest common factor. Without the most fundamental identity, nothing could exist. Therefore God is omnipotent.

The G factor distributes over the sum of all that exists. Therefore G is omnipresent.

Since there is only one greatest common factor. God is a monic entity.

A definition that agrees with monotheism?