The most effective proof that there exists a non-computable function from N to N

The most effective proof that there exists a non-computable function from N to N | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 11 July 2025 V1 Latest version Share on The most effective proof that there exists a non-computable function from N to N Author : Apoloniusz Tyszka 0000-0002-2770-5495 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175225951.18891698/v1 247 views 121 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract For n∈N, f(n) denotes the smallest b∈N such that if a system of equations S⊆{1=x_k, x_i+x_j=x_k, x_i·x_j=x_k: i,j,k∈{0,...,n}} has a solution in N^{n+1}, then S has a solution in {0,...,b}^{n+1}. The author proved earlier that the function f:N→N is computable in the limit and eventually dominates every computable function g:N→N. We present a simple code in MuPAD which for n∈N prints the sequence {f_i(n)}_{i=0}^∞ of non-negative integers converging to f(n). Supplementary Material File (a_tyszka_july_11.pdf) Download 313.23 KB Information & Authors Information Version history V1 Version 1 11 July 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords computable function eventual domination limit-computable function mupad semi-algorithm Authors Affiliations Apoloniusz Tyszka 0000-0002-2770-5495 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 247 views 121 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Apoloniusz Tyszka. The most effective proof that there exists a non-computable function from N to N. Authorea . 11 July 2025. DOI: https://doi.org/10.22541/au.175225951.18891698/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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