I found an interesting math result, but now I see a contradiction

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SUMMARY

The discussion centers on a claimed resolution of the halting problem, suggesting it is "essentially solvable." However, contradictions arise when referencing Peano Arithmetic and Gödel's incompleteness theorem, leading to a critique of faith-based arguments in mathematical discourse. The conversation highlights the importance of adhering to scientific principles in mathematical discussions, as emphasized by forum guidelines. The thread concluded with a reminder to maintain a focus on empirical evidence rather than faith.

PREREQUISITES
  • Understanding of the halting problem in computer science
  • Familiarity with Gödel's incompleteness theorems
  • Knowledge of Peano Arithmetic and its implications
  • Awareness of scientific discourse guidelines in academic forums
NEXT STEPS
  • Research the implications of Gödel's incompleteness theorem on mathematical logic
  • Explore the foundations of Peano Arithmetic and its applications
  • Study the halting problem in depth, including its significance in computer science
  • Review guidelines for scientific discussions in academic forums
USEFUL FOR

Mathematicians, computer scientists, and anyone engaged in theoretical discussions about the foundations of mathematics and logic.

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I found an interesting math result ("halting problem is essentially solvable") yesterday, but now I see a contradiction (it follows "halting problem is solvable"). Participate in finding my error.
I found an interesting math result ("halting problem is essentially solvable") yesterday, but now I see a contradiction (it follows "halting problem is solvable"). Participate in finding my error.

Here is my short yesterday article (with links to other yesterday articles):

[Unacceptable reference redacted by the Mentors]
 
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Mathematics news on Phys.org
I've found an error myself:

In the linked article [Unacceptable reference redacted by the Mentors] I describe the error in bold font.

The linked article nevertheless had another valid very interesting result that replaces the paradigm that mathematics is theorem proving by another paradigm.

You have a new release of mathematics.
 
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I glanced at the article, and found that it referenced your prior article on using Peano Arithmetic to avoid Godel's incompleteness result ##-## the only 'support' in that article for your contention was 'faith'; not science. Please understand that PF is a set of forums for science; not for exploring faith-based ideas about scientific and mathematical matters. Please read the guidelines, and if you have questions or concerns about any of them, please PM one of the Mentors.
 
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And with that helpful reply by @sysprog the thread is now closed.
 
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