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  1.  11
    Application of "A Thing Exists If It's A Grouping" to Russell's Paradox and Godel's First Incompletness Theorem.Roger Granet - manuscript
    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, (...)
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  2.  20
    Do Abstract Mathematical Axioms About Infinite Sets Apply To The Real, Physical Universe?Roger Granet - manuscript
    In mathematics, if one starts with the infinite set of positive integers, P, and want to compare the size of the subset of odd positives, O, with P, this is done by pairing off each odd with a positive, using a function such as P=2O+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the set of positives are the same size, or have the same cardinality. This counter-intuitive result ignores (...)
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  3.  9
    Infinite Sets: The Appearance of an Infinite Set Depends on the Perspective of the Observer.Roger Granet - manuscript
    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 to a (...)
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  4.  42
    Proposed Solutions to the Questions "Why Does a Thing Exist?" and "Why is There Something Rather Than Nothing?".Roger Granet - manuscript
    A solution to the question "Why is there something rather than nothing?" is proposed that also entails a proposed solution to the question "Why do things exist?". In brief, I propose that a thing exists if it is a grouping. A grouping ties stuff together into a unit whole and is visually seen and physically or mentally present as an edge, boundary, or enclosing surface that defines what is tied together into the unit whole and that, therefore, defines what is (...)
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