Wikipedia:Articles for deletion/Non-integer representation

Non-integer representation

(Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL)

Article has no sources and appears to be WP:original research, only one such system (golden ratio base) appears to have been studied by WP:reliable sources and it already has its own article. — sligocki (talk) 00:09, 11 November 2009 (UTC)[reply]

Comment - This would seem to be an AfD that requires expert assistance. I'm unaware of the best procedure for getting the attention of the mathematics editors but if someone passing through knows it could they jump up and down and wave their hands on the relevant pages? - DustFormsWords (talk) 00:16, 11 November 2009 (UTC)[reply]
- Sounds good. I posted a notice to Wikipedia talk:WikiProject Mathematics. I think that would be the right place. Cheers, — sligocki (talk) 00:28, 11 November 2009 (UTC)[reply]
Keep. A significant portion of §4.1 in Donald Knuth's The Art of Computer Programming is devoted to non-integer bases. This easily establishes their notability. Le Docteur (talk) 01:51, 11 November 2009 (UTC)[reply]

Also this American Scientist article discusses base e somewhat. Le Docteur (talk) 02:12, 11 November 2009 (UTC)[reply]

Studied more seriously in Parry, W. (1960), "On the β-expansions of real numbers", Acta Mathematica Academiae Scientiarum Hungaricae, 11: 401–416, ISSN 0001-5954, MR 0142719. Le Docteur (talk) 02:24, 11 November 2009 (UTC)[reply]

More recent article, with literature review: Glendinning, Paul; Sidorov, Nikita (2001), "Unique representations of real numbers in non-integer bases", Mathematical Research Letters, 8 (4): 535–543, ISSN 1073-2780, MR 1851269 Le Docteur (talk) 02:53, 11 November 2009 (UTC)[reply]

Various example bases (with emphasis on the golden ratio, though) are considered in Frougny, Christiane, "How to write integers in non-integer base", LATIN '92, Lecture Notes in Computer Science, doi:10.1007/BFb0023811, ISBN 978-3-540-55284-0, ISSN 0302-9743 {{citation}}: Unknown parameter |Pages= ignored (|pages= suggested) (help); Unknown parameter |Publisher= ignored (|publisher= suggested) (help); Unknown parameter |Volume= ignored (|volume= suggested) (help). Le Docteur (talk) 12:24, 11 November 2009 (UTC)[reply]

Comment. I have added the above references to the article, and expanded the article to include some content from these references. There is still a lot of work to be done, though. Le Docteur (talk) 14:44, 11 November 2009 (UTC)[reply]

Keep per Le Docteur. I believe it's best to merge the article into Non-standard positional numeral systems, but since the topic is clearly notable that's not something that needs to be decided by this AfD. Hans Adler 06:35, 11 November 2009 (UTC)[reply]

The references provided by Le Docteur convince me the subject is sufficiently notable to have an article. — Carl (CBM · talk) 14:02, 11 November 2009 (UTC)[reply]
I'm leaning toward keep, myself. I've only read about phinary and Knuth's quarter-imaginary base, but I imagine that with the references above we can dig out more. Also, it might help prevent the creep of many permastubs on their own non-integer bases -- they can just get a section here. CRGreathouse (t | c) 14:47, 11 November 2009 (UTC)[reply]

Keep "e" is likely the best-known example, as Le Docteur points out. Collect (talk) 14:51, 11 November 2009 (UTC)[reply]

Comment. I was also of this impression, but I am having difficulty digging up references to the effect. I know that expansions in the base e have some special "ergodic" properties that make them particularly significant, but I can't find any references that state this clearly. Any help would be appreciated. Le Docteur (talk) 15:09, 11 November 2009 (UTC)[reply]

Keep. I always thought of this as a cute recreational math topic. I'm actually surprised to learn that there are several applications (the only one I ever heard of was in information theory; supposedly base e is the "most efficient" in some sense that wasn't explained); Le Docteur's efforts above demonstrate, I think, that the subject is notable even among professional researchers. Ozob (talk) 16:12, 11 November 2009 (UTC)[reply]