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A New Set Theory for Analysis
[post]

2019
unpublished

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We

doi:10.20944/preprints201901.0089.v1
fatcat:ig2qigpujzbk7l6iuw3t56no5e