## Proof of the Existence of Transfinite Cardinals Strictly Smaller Than Aleph Zero with an Ensuing Solution to the Twin Prime Conjecture

**Authors:** Karan Doshi

In this paper the author submits a proof using the Power Set relation for the existence of a transfinite cardinal strictly smaller than Aleph Zero, the cardinality of the Naturals. Further, it can be established taking these arguments to their logical conclusion that even smaller transfinite cardinals exist. In addition, as a lemma using these new found and revolutionary concepts, the author conjectures that some outstanding unresolved problems in number theory can be brought to heel. Specifically, a proof of the twin prime conjecture is given.

**Comments:** 11 Pages.

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### Submission history

[v1] 2014-12-19 02:03:14

[v2] 2015-01-27 21:14:44

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