A mathematical thought experiment for accepting the continuum hypothesis
The article explores the theoretical implications of considering the continuum hypothesis a fundamental axiom in mathematics, potentially impacting mathematical reasoning and structures. Alternative foundational schemes and implications of historical developments are discussed.
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The article discusses a historical thought experiment on how the continuum hypothesis could have been considered a fundamental axiom in mathematics, essential even for calculus. It explores the idea that viewing the continuum hypothesis as a necessary axiom could have significant implications for the field. Comments on the article suggest alternative foundational schemes and question the possibility of adopting axioms inconsistent with ZFC. The discussion touches on the implications of different historical developments on mathematical axioms and their consequences. Overall, the article delves into the theoretical implications of the continuum hypothesis as a fundamental axiom and its potential impact on mathematical reasoning and structures.
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4 commentsFor an actual thought experiment that rejects the continuum hypothesis, I rather enjoy the explanation found at:
https://risingentropy.com/the-continuum-hypothesis-is-false/
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