# Roger Granet

Areas of Specialization
Areas of Interest
•  194
##### Why does a thing exist? and Why is there something rather than nothing?
An age-old proposal that to be is to be a unity, or what I call a grouping, is updated and applied to the question “Why is there something rather than nothing?” (WSRTN). I propose that a thing exists if it is a grouping. A grouping (i.e., a unity, one) ties zero or more things together into a new unit whole and existent entity. An example of a grouping of zero things is the empty set. Next, in regard to WSRTN, when we subtract away all existent entities (matter, energy, time, space/volume, co…Read more
•  60
##### Do Abstract Mathematical Axioms About Infinite Sets Apply To The Real, Physical Universe?
Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of positives are the same size, or ha…Read more
•  58
##### Application of "A Thing Exists If It's A Grouping" to Russell's Paradox and Godel's First Incompletness Theorem
A resolution to the Russell Paradox is presented that is similar to Russell's “theory of types” method but is instead based on the definition of why a thing exists as described in previous work by this author. In that work, it was proposed that a thing exists if it is a grouping tying "stuff" together into a new unit whole. In tying stuff together, this grouping defines what is contained within the new existent entity. A corollary is that a thing, such as a set, does not exist until after the…Read more
•  53
##### Infinite Sets: The Appearance of an Infinite Set Depends on the Perspective of the Observer
Given an infinite set of finite-sized spheres extending in all directions forever, a finite-sized (relative to the spheres inside the set) observer within the set would view the set as a space composed of discrete, finite-sized objects. A hypothetical infinite-sized (relative to the spheres inside the set) observer would view the set as a continuous space and would see no distinct elements within the set. Using this analogy, the mathematics of infinities, such as the assignment of a cardinality…Read more