{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T02:39:07Z","timestamp":1777516747435,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2016,7,14]],"date-time":"2016-07-14T00:00:00Z","timestamp":1468454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Computability"],"published-print":{"date-parts":[[2017,8,7]]},"abstract":"<jats:p>We consider various ways to represent irrational numbers by subrecursive functions: via Cauchy sequences, Dedekind cuts, trace functions, several variants of sum approximations and continued fractions. Let [Formula: see text] be a class of subrecursive functions. The set of irrational numbers that can be obtained with functions from [Formula: see text] depends on the representation. We compare the sets obtained by the different representations.<\/jats:p>","DOI":"10.3233\/com-160063","type":"journal-article","created":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T12:23:18Z","timestamp":1468585398000},"page":"249-276","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":12,"title":["On subrecursive representability of irrational numbers"],"prefix":"10.1177","volume":"6","author":[{"given":"Lars","family":"Kristiansen","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO-0316 Oslo, Norway"},{"name":"Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, NO-0316 Oslo, Norway."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,7,14]]},"reference":[{"key":"ref001","unstructured":"O.\u00a0Aberth, Computable Analysis, MacGraw-Hill, New York, 1980."},{"key":"ref002","unstructured":"S.B.\u00a0Cooper, Computability Theory, CRC Press, Boca Raton, 2004."},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.201400013"},{"key":"ref004","unstructured":"A.Y.\u00a0Khintchine, Continued Fractions, P. Noordhoff, Ltd, Groningen, The Netherlands, 1963. (Translated by Peter Wynn.)"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01744572"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(86)90154-4"},{"key":"ref007","doi-asserted-by":"crossref","unstructured":"L.\u00a0Kristiansen, Information content and computational complexity of recursive sets, in: G\u00f6del \u201996, P.\u00a0Hajek, ed. 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