Add resource "What Gödel Discovered" Accepted
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Add What Gödel Discovered
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 What Gödel Discovered
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 Web
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 202011
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 In 1931, a 25yearold Kurt Gödel wrote a proof that turned mathematics upside down. The implication was so astounding, and his proof so elegant that it was...kind of funny. I wanted to share his discovery with you. Fair warning though, I’m not a mathematician; I’m a programmer. This means my understanding is intuitive and not exact. Hopefully, that will come to our advantage since I have no choice but to avoid formality.
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 https://stopa.io/post/269
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 no value
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Add Gödel's incompleteness theorems
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 Gödel's incompleteness theorems
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 Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system capable of modelling basic arithmetic. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.
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 https://en.wikipedia.org/?curid=58863
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Add Hilbert's program
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 Hilbert's program
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 In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel's incompleteness theorems, published in 1931, showed that Hilbert's program was unattainable for key areas of mathematics.
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 https://en.wikipedia.org/?curid=607286
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Add Gödel's incompleteness theorems is applicable to What Gödel Discovered
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Add Hilbert's program is applicable to What Gödel Discovered
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Add Gödel's incompleteness theorems relates to Hilbert's program
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