A question that the physics community is asking today, is, “What is a Singularity?”, and “Are Singularities Detectable and Measurable?” This work, will describe five (5) different types or classifications of “Singularities” in nature: the Inverse Distance Power Law Singularity, the Physical Singularity, the Naked Singularity, the Coordinate Singularity, and the Big Bang Singularity. Correlating the nature of these singularities, with the mathematics, theory, and the real physical world, is a conundrum in physics. This work extends the “Strong and Weak Cosmic Censorship” hypotheses originally proposed an debated by Roger Penrose, Steven Hawking, and Kip Thorne, by adding an additional thirteen (13) “Censorships” which removes some of the contradiction that exists with just the two (2) original “Cosmic Censorship Hypotheses” alone. The “Penrose–Hawking–Thorne” singularity theorems, of General Relativity Theory, described in this work, addresses mathematically the concept of “Geodesic Incompleteness”; which is another name for a geodesic with infinite curvature, which at one end of the geodesic is a singularity. And “Geodesic Completeness” another name for a geodesic with infinite curvature, on a 2-Sphere Riemann Manifold; there the Non-Euclidean geometry still predicts a singularity.