Infinite Sets: The Appearance of an Infinite Set Depends on the Perspective of the Observer

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Abstract
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 set, depends on the reference frame of the observer thinking about them (the mind of the mathematician) relative to the infinite set. This reasoning may also relate to the differing views of space in relativity as continuous and in quantum mechanics as discrete.
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Archival date: 2021-10-12
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