On the Nature of N-Dimensional Mathematical Objects, with n ≥ 0
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- Continuum, Point, Line, N-Dimensional Objects, Set Theory, Power Set, Cardinality
- Antonio Luigi Paolilli
- In the Aristotelian viewpoint a line cannot be made by points. The debate on the nature of the continuum has lasted for centuries till the present time. The prevailing opinion is that lines are generated by the movement of points, planes by the movement of lines and so on. In this paper we will try to clarify the nature of the relation between points and other geometric objects taking into account the actual nature of each individual object. In this way we will show that the generation process of geometric objects is opposite to the prevailing opinion mentioned above. We will also introduce a question about the relation between sets and power sets, which in our opinion is similar to the relation among geometric objects with a different number of dimensions, although the generation process of sets and power sets is the opposite of the geometrical objects' one. We sustain that power sets seem greater than sets since, so as they have been defined, they have an additional dimension, here defined Event axis. In a short appendix it is shown how the set of points of a n-dimensional geometric object (with n > 1) may be put in a biunivocal correspondence even with a single point.
Full text: IJISM_839_FINAL.pdf