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Everything about Continuum hypothesis
Proposition in mathematical logic
In mathematics, specifically set theory, the continuum hypothesis is a hypothesis about the possible sizes of infinite sets. It states:There is no set whose cardinality is strictly between that of the integers and the real numbers. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Continuum hypothesisA 5-minute orientation
- Skim a recent paper: Testing the Kerr Black Hole Hypothesis with GRS 1716-249 by Combining the Continuum Fitting and the Iron-line MethodsInfluential work since 2022
- Pick up a classic book: Real Numbers, Generalizations of the Reals, and Theories of ContinuaThe most-reprinted book on the subject
- Read the landmark paper: Reconciling niche and neutrality: the continuum hypothesisCited 720 times
- Go sideways: Aleph numberA closely related topic
- Go sideways: List of statements independent of ZFCA closely related topic
📖 Definitions
Noun The hypothesis which states that any infinite subset of ℝ must have the cardinality of either the set of natural numbers or of ℝ itself.
Noun The assumption, for the purposes of mathematical modelling, that the material being studied is a continuous mass rather than being composed of discrete particles.
🏆 Landmark papers (most cited)
Reconciling niche and neutrality: the continuum hypothesis
THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
Noninvasive Neuromodulation with Ultrasound? A Continuum Mechanics Hypothesis
Measurable cardinals and the continuum hypothesis
THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS, II
Consistency-Proof for the Generalized Continuum-Hypothesis
Higher Souslin trees and the generalized continuum hypothesis
The Generalized Continuum Hypothesis Can Fail Everywhere
🆕 Influential since 2022
Testing the Kerr Black Hole Hypothesis with GRS 1716-249 by Combining the Continuum Fitting and the Iron-line Methods
Testing the Kerr black hole hypothesis with the continuum-fitting and the iron line methods: the case of GRS 1915+105
Exploring the Hypothesis of a Schizophrenia and Bipolar Disorder Continuum: Biological, Genetic and Pharmacologic Data
A Paradigmatic Case of Genetic Overlap Between Neurodevelopment Disorders and Schizophrenia Aligning with the Neurodevelopmental Continuum Hypothesis
Development of number sense and numeration: a continuum hypothesis
📚 Books worth reading
Real Numbers, Generalizations of the Reals, and Theories of ContinuaP. Ehrlich · 1899
Set theory and the continuum problemRaymond M. Smullyan, Melvin Fitting · 1996- 📕Forcing for MathematiciansNik Weaver · 2014
Set theory and the continuum hypothesisPaul J. Cohen · 1966- 📕Logic numbers and the continuum hypothesisLere Shakunle · 1991
Set theory and the continuum hypothesesPaul J. Cohen · 2008- 📕Understanding evidenceRichard W. Puddy · 2011
- 📕The evidence project overviewNational Center for Injury Prevention and Control (U.S.). Division of Violence Prevention · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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