R is the multiset [ai,aj…] of fundamental components comprising the entirety of everything that exists.

Assigning a precise definition to the concept of nothingness has proved challenging in both physics and philosophy. In quantum mechanics, "nothing" often denotes the ground state, while in philosophy, it can signify the absence of properties or qualities. It turns out that neither of these definitions can encompass a non-contradictory meaning of the term. Consider the case were only two particles ai and aj exist ontologically (R=[ai,aj]). If space itself is composed of elements of R, a “fabric of space” if you will, then there cannot be a void between the elements of R, thus everything that exists would necessarily form a perfectly solid object. This does not match observation. On the contrary, if space itself is not composed of the elements of R, then it doesn’t exist, and therefore Nothing (N) equates to Empty Space. Notice that you cannot remove the spatial component of N, and therefore it is necessary to describe it mathematically which is most easily done with vector spaces. To do so, suppose that N ⊊ ℝn. It follows that ℝn\N is neither something (elements of R) nor nothing resulting in a contradiction. It follows that N is unbounded spatially, and therefore, for some n>=3, N=ℝn.

Let R=[ai]. In order for ai to be produced from nothing, it must be constructed out of points in space. Since any collection of points in space don’t form an ontological object, ai cannot be produced from them. Thus, something cannot be produced from nothing. It follows that the elements of R can only be organized or rearranged to produce composite objects, therefore referencing them as fundamental is justified.