**Authors:** Roger Granet

This paper discusses how an infinite set would appear to different observers and how this applies to both physics and mathematics. Consider a set, N, defined as containing an infinite number of discrete, finite-sized elements such as balls. Any one of these balls can be defined as an internal observer, O. The balls extend outward in infinite numbers relative to any location and orientation of any internal observer O. That is, wherever O is in the set and in whichever direction O is “looking”, the elements of the set extend without bounds the same potentially infinite distance in all directions relative to O. To observer O, set N appears as a potentially infinite space composed of discrete, finite-sized elements. Now, consider a hypothetical second observer, P who is outside the same set N and whose size relative to internal observer O is actually infinite. That is, P is of the same size “scale” as the entire set N, which is actually infinite relative to O. To observer P, each ball O is infinitesimally small, so that P can not distinguish the boundary of each ball O. Therefore, to P, set N appears as a finite-sized object containing a smooth, infinitely divisible internal space. The implications of these differing views of the same set depending on the reference frame of the observer are discussed for both mathematics and physics.

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[v1] 2016-12-17 23:45:41

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