•  51
    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
  •  51
    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
  •  57
    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
  •  188
    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 ties zero or more things together into a new unit whole and existent entity and is similar in meaning to the more familiar terms unity, one, and aggregate. An example of tying zero things together is the empty set. Next, in regard to WSRTN, when we subtract away all…Read more