jostylr/Reals-as-Oracles
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This is a paper for a new definition of real numbers, namely, viewing a real number as an oracle that affirms when a rational interval contains the real number.
8 mentions on Hacker News by 1 person: 0 stories, 8 comments · first 2023-07-22 · latest 2025-08-14
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…is often used by constructivists and can be thought of viewing a real number as a measurement. 1: https://github.com/jostylr/Reals-as-Oracles
comment by jostylr · 2025-08-14 · in What are the real numbers, really? (2024) -
…skirt around the issue that this is defining the real number. My work on this is hosted on GitHub: https://github.com/jostylr/Reals-as-Oracles
comment by jostylr · 2025-05-03 · in Mathematician solves algebra's oldest problem using intriguing number sequences -
…recent version going over what I just said is Real Numbers As Rational Betweenness Relations [2] 2: https://github.com/jostylr/Reals-as-Oracles/ 1: https://github.com/jostylr/Reals-as-Oracles/blob/a98472813e9...
comment by jostylr · 2025-02-18 · in Dedekind's Subtle Knife -
…the simplified cut property of that paper was a pleasant pathway to establishing completeness. [1]: https://github.com/jostylr/Reals-as-Oracles/blob/main/articl...
comment by jostylr · 2025-02-18 · in Dedekind's Subtle Knife -
…procedure for figuring out whether an interval contains the number or not. The work is hosted at ( https://github.com/jostylr/Reals-as-Oracles ) with the first paper in the readme being the most recent version of this idea. The older and…
comment by jostylr · 2025-02-17 · in “A calculator app? Anyone could make that” -
…into the practical messiness of not being able to fully present a real number in practice[2]. 1: https://github.com/jostylr/Reals-as-Oracles/blob/main/articl... 2: https://github.com/jostylr/Reals-as-Oracles/blob/main/articl...
comment by jostylr · 2024-12-31 · in “A Course of Pure Mathematics” – G. H. Hardy (1921) [pdf] -
…point is the real number). If curious for details, my paper repository on this matter is at https://github.com/jostylr/Reals-as-Oracles where I not only prove that it all works out as it should, but also give an example of doing continued…
comment by jostylr · 2023-08-16 · in Decimal to fraction -
…oracles, define an arithmetic, and prove that they satisfy the axioms of real numbers. For details: https://github.com/jostylr/Reals-as-Oracles/ In many ways, this is giving a definitional support to the use of interval analysis which is,…
comment by jostylr · 2023-07-22 · in About math limitations