Division by zero (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Division by zero" in English language version.

refsWebsite

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18doi.org

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6jstor.org

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4archive.org

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3semanticscholar.org

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1youtube.com

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1ias.ac.in

6,086^th place

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1openstax.org

6,581^st place

3,967^th place

1worldcat.org

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1wisc.edu

1,045^th place

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1books.google.com

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1harvard.edu

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1su.se

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1arm.com

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1handle.net

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1python.org

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1,903^rd place

1arxiv.org

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1xenaproject.wordpress.com

low place

1wired.com

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1web.archive.org

1^st place

1berkeley.edu

580^th place

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archive.org (Global: 6^th place; English: 6^th place)

Kochenburger, Ralph J.; Turcio, Carolyn J. (1974), Computers in Modern Society, Santa Barbara: Hamilton, Some other operations, including division, can also be performed by the desk calculator (but don't try to divide by zero; the calculator never will stop trying to divide until stopped manually).
For a video demonstration, see: What happens when you divide by zero on a mechanical calculator?, 7 Mar 2021, retrieved 2024-01-06 – via YouTube
Bunch 1982, p. 14 Bunch, Bryan (1982), Mathematical Fallacies and Paradoxes, New York: Van Nostrand Reinhold, ISBN 0-442-24905-5 (Dover reprint 1997)
Kaplan, Robert (1999), The Nothing That Is: A Natural History of Zero, New York: Oxford University Press, pp. 68–75, ISBN 978-0-19-514237-2
Bunch 1982, p. 15 Bunch, Bryan (1982), Mathematical Fallacies and Paradoxes, New York: Van Nostrand Reinhold, ISBN 0-442-24905-5 (Dover reprint 1997)

arm.com (Global: 4,773^rd place; English: 3,130^th place)

developer.arm.com

"Divide instructions", ARMv7-M Architecture Reference Manual (Version D ed.), Arm Limited, 2010, retrieved 2024-06-12

arxiv.org (Global: 69^th place; English: 59^th place)

Tanter, Éric; Tabareau, Nicolas (2015), "Gradual certified programming in coq", DLS 2015: Proceedings of the 11th Symposium on Dynamic Languages, Association for Computing Machinery, arXiv:1506.04205, doi:10.1145/2816707.2816710, The standard division function on natural numbers in Coq, div, is total and pure, but incorrect: when the divisor is 0, the result is 0.

berkeley.edu (Global: 580^th place; English: 462^nd place)

cs.berkeley.edu

William Kahan (14 Oct 2011), Desperately Needed Remedies for the Undebuggability of Large Floating-Point Computations in Science and Engineering (PDF)

books.google.com (Global: 3^rd place; English: 3^rd place)

Conway, John H. (2000) [1976], On Numbers and Games (2nd ed.), CRC Press, p. 20, ISBN 9781568811277

doi.org (Global: 2^nd place; English: 2^nd place)

Zazkis & Liljedahl 2009, p. 52–53. Zazkis, Rina; Liljedahl, Peter (2009), "Stories that explain", Teaching Mathematics as Storytelling, Sense Publishers, pp. 51–65, doi:10.1163/9789087907358_008, ISBN 978-90-8790-734-1
Zazkis & Liljedahl 2009, p. 55–56. Zazkis, Rina; Liljedahl, Peter (2009), "Stories that explain", Teaching Mathematics as Storytelling, Sense Publishers, pp. 51–65, doi:10.1163/9789087907358_008, ISBN 978-90-8790-734-1
Zazkis & Liljedahl 2009, pp. 53–54, gives an example of a king's heirs equally dividing their inheritance of 12 diamonds, and asks what would happen in the case that all of the heirs died before the king's will could be executed. Zazkis, Rina; Liljedahl, Peter (2009), "Stories that explain", Teaching Mathematics as Storytelling, Sense Publishers, pp. 51–65, doi:10.1163/9789087907358_008, ISBN 978-90-8790-734-1
In China, Taiwan, and Japan, school textbooks typically distinguish between the ratio ⁠ $N:D$ ⁠ and the value of the ratio ⁠ ${\tfrac {N}{D}}$ ⁠. By contrast in the USA textbooks typically treat them as two notations for the same thing.
Lo, Jane-Jane; Watanabe, Tad; Cai, Jinfa (2004), "Developing Ratio Concepts: An Asian Perspective", Mathematics Teaching in the Middle School, 9 (7): 362–367, doi:10.5951/MTMS.9.7.0362, JSTOR 41181943
Cengiz, Nesrin; Rathouz, Margaret (2018), "Making Sense of Equivalent Ratios", Mathematics Teaching in the Middle School, 24 (3): 148–155, doi:10.5951/mathteacmiddscho.24.3.0148, JSTOR 10.5951/mathteacmiddscho.24.3.0148, S2CID 188092067
Clark, Matthew R.; Berenson, Sarah B.; Cavey, Laurie O. (2003), "A comparison of ratios and fractions and their roles as tools in proportional reasoning", The Journal of Mathematical Behavior, 22 (3): 297–317, doi:10.1016/S0732-3123(03)00023-3
Cheng, Ivan (2010), "Fractions: A New Slant on Slope", Mathematics Teaching in the Middle School, 16 (1): 34–41, doi:10.5951/MTMS.16.1.0034, JSTOR 41183440
Cavey, Laurie O.; Mahavier, W. Ted (2010), "Seeing the potential in students' questions", The Mathematics Teacher, 104 (2): 133–137, doi:10.5951/MT.104.2.0133, JSTOR 20876802
Wegman, Edward J.; Said, Yasmin H. (2010), "Natural homogeneous coordinates", Wiley Interdisciplinary Reviews: Computational Statistics, 2 (6): 678–685, doi:10.1002/wics.122, S2CID 121947341
Robinson, K. M.; LeFevre, J. A. (2012), "The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework", Educational Studies in Mathematics, 79 (3): 409–428, doi:10.1007/s10649-011-9330-5, JSTOR 41413121
Cheng 2023, p. 78; Zazkis & Liljedahl 2009, p. 55 Cheng, Eugenia (2023), Is Math(s) Real? How Simple Questions Lead Us to Mathematics' Deepest Truths, Basic Books, ISBN 978-1-541-60182-6 Zazkis, Rina; Liljedahl, Peter (2009), "Stories that explain", Teaching Mathematics as Storytelling, Sense Publishers, pp. 51–65, doi:10.1163/9789087907358_008, ISBN 978-90-8790-734-1
Zazkis & Liljedahl 2009, p. 55. Zazkis, Rina; Liljedahl, Peter (2009), "Stories that explain", Teaching Mathematics as Storytelling, Sense Publishers, pp. 51–65, doi:10.1163/9789087907358_008, ISBN 978-90-8790-734-1
Roy, Rahul (Jan 2003), "Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science", Resonance, 8 (1): 30–40, doi:10.1007/BF02834448
Cajori, Florian (1929), "Absurdities due to division by zero: An historical note", The Mathematics Teacher, 22 (6): 366–368, doi:10.5951/MT.22.6.0366, JSTOR 27951153.
Carlström, Jesper (2004), "Wheels: On Division by Zero", Mathematical Structures in Computer Science, 14 (1): 143–184, doi:10.1017/S0960129503004110
Cody, W. J. (Mar 1981), "Analysis of Proposals for the Floating-Point Standard", Computer, 14 (3): 65, doi:10.1109/C-M.1981.220379, S2CID 9923085, With appropriate care to be certain that the algebraic signs are not determined by rounding error, the affine mode preserves order relations while fixing up overflow. Thus, for example, the reciprocal of a negative number which underflows is still negative.
Wang, Xi; Chen, Haogang; Cheung, Alvin; Jia, Zhihao; Zeldovich, Nickolai; Kaashoek, M. Frans, "Undefined behavior: what happened to my code?", APSYS '12: Proceedings of the Asia-Pacific Workshop on Systems, APSYS '12, Seoul, 23–24 July 2012, New York: Association for Computing Machinery, doi:10.1145/2349896.2349905, hdl:1721.1/86949, ISBN 978-1-4503-1669-9
Tanter, Éric; Tabareau, Nicolas (2015), "Gradual certified programming in coq", DLS 2015: Proceedings of the 11th Symposium on Dynamic Languages, Association for Computing Machinery, arXiv:1506.04205, doi:10.1145/2816707.2816710, The standard division function on natural numbers in Coq, div, is total and pure, but incorrect: when the divisor is 0, the result is 0.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Wang, Xi; Chen, Haogang; Cheung, Alvin; Jia, Zhihao; Zeldovich, Nickolai; Kaashoek, M. Frans, "Undefined behavior: what happened to my code?", APSYS '12: Proceedings of the Asia-Pacific Workshop on Systems, APSYS '12, Seoul, 23–24 July 2012, New York: Association for Computing Machinery, doi:10.1145/2349896.2349905, hdl:1721.1/86949, ISBN 978-1-4503-1669-9

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Gbur, Greg (2011), Mathematical Methods for Optical Physics and Engineering, Cambridge University Press, pp. 88–93, Bibcode:2011mmop.book.....G, ISBN 978-0-521-51610-5

ias.ac.in (Global: 6,086^th place; English: 4,310^th place)

Roy, Rahul (Jan 2003), "Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science", Resonance, 8 (1): 30–40, doi:10.1007/BF02834448

jstor.org (Global: 26^th place; English: 20^th place)

In China, Taiwan, and Japan, school textbooks typically distinguish between the ratio ⁠ $N:D$ ⁠ and the value of the ratio ⁠ ${\tfrac {N}{D}}$ ⁠. By contrast in the USA textbooks typically treat them as two notations for the same thing.
Lo, Jane-Jane; Watanabe, Tad; Cai, Jinfa (2004), "Developing Ratio Concepts: An Asian Perspective", Mathematics Teaching in the Middle School, 9 (7): 362–367, doi:10.5951/MTMS.9.7.0362, JSTOR 41181943
Cengiz, Nesrin; Rathouz, Margaret (2018), "Making Sense of Equivalent Ratios", Mathematics Teaching in the Middle School, 24 (3): 148–155, doi:10.5951/mathteacmiddscho.24.3.0148, JSTOR 10.5951/mathteacmiddscho.24.3.0148, S2CID 188092067
Cheng, Ivan (2010), "Fractions: A New Slant on Slope", Mathematics Teaching in the Middle School, 16 (1): 34–41, doi:10.5951/MTMS.16.1.0034, JSTOR 41183440
Cavey, Laurie O.; Mahavier, W. Ted (2010), "Seeing the potential in students' questions", The Mathematics Teacher, 104 (2): 133–137, doi:10.5951/MT.104.2.0133, JSTOR 20876802
Robinson, K. M.; LeFevre, J. A. (2012), "The inverse relation between multiplication and division: Concepts, procedures, and a cognitive framework", Educational Studies in Mathematics, 79 (3): 409–428, doi:10.1007/s10649-011-9330-5, JSTOR 41413121
Cajori, Florian (1929), "Absurdities due to division by zero: An historical note", The Mathematics Teacher, 22 (6): 366–368, doi:10.5951/MT.22.6.0366, JSTOR 27951153.

openstax.org (Global: 6,581^st place; English: 3,967^th place)

Herman, Edwin; Strang, Gilbert; et al. (2023), "2.2 The Limit of a Function", Calculus, vol. 1, Houston: OpenStax, p. 454, ISBN 978-1-947172-13-5, OCLC 1022848630

python.org (Global: 2,232^nd place; English: 1,903^rd place)

docs.python.org

"Built-in Exceptions", Python 3 Library Reference, Python Software Foundation, § "Concrete exceptions – exception ZeroDivisionError", retrieved 2024-01-22

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Cengiz, Nesrin; Rathouz, Margaret (2018), "Making Sense of Equivalent Ratios", Mathematics Teaching in the Middle School, 24 (3): 148–155, doi:10.5951/mathteacmiddscho.24.3.0148, JSTOR 10.5951/mathteacmiddscho.24.3.0148, S2CID 188092067
Wegman, Edward J.; Said, Yasmin H. (2010), "Natural homogeneous coordinates", Wiley Interdisciplinary Reviews: Computational Statistics, 2 (6): 678–685, doi:10.1002/wics.122, S2CID 121947341
Cody, W. J. (Mar 1981), "Analysis of Proposals for the Floating-Point Standard", Computer, 14 (3): 65, doi:10.1109/C-M.1981.220379, S2CID 9923085, With appropriate care to be certain that the algebraic signs are not determined by rounding error, the affine mode preserves order relations while fixing up overflow. Thus, for example, the reciprocal of a negative number which underflows is still negative.

su.se (Global: low place; English: low place)

www2.math.su.se

Carlström, Jesper (2004), "Wheels: On Division by Zero", Mathematical Structures in Computer Science, 14 (1): 143–184, doi:10.1017/S0960129503004110

web.archive.org (Global: 1^st place; English: 1^st place)

Stutz, Michael (24 Jul 1998), "Sunk by Windows NT", Wired News, archived from the original on 1999-04-29

wired.com (Global: 193^rd place; English: 152^nd place)

Stutz, Michael (24 Jul 1998), "Sunk by Windows NT", Wired News, archived from the original on 1999-04-29

wisc.edu (Global: 1,045^th place; English: 746^th place)

people.math.wisc.edu

Keisler, H. Jerome (2023) [1986], Elementary Calculus: An Infinitesimal Approach, Prindle, Weber & Schmidt, pp. 29–30

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Herman, Edwin; Strang, Gilbert; et al. (2023), "2.2 The Limit of a Function", Calculus, vol. 1, Houston: OpenStax, p. 454, ISBN 978-1-947172-13-5, OCLC 1022848630

xenaproject.wordpress.com (Global: low place; English: low place)

Buzzard, Kevin (5 Jul 2020), "Division by zero in type theory: a FAQ", Xena Project (Blog), retrieved 2024-01-21

youtube.com (Global: 9^th place; English: 13^th place)

Kochenburger, Ralph J.; Turcio, Carolyn J. (1974), Computers in Modern Society, Santa Barbara: Hamilton, Some other operations, including division, can also be performed by the desk calculator (but don't try to divide by zero; the calculator never will stop trying to divide until stopped manually).
For a video demonstration, see: What happens when you divide by zero on a mechanical calculator?, 7 Mar 2021, retrieved 2024-01-06 – via YouTube

Division by zero (English Wikipedia)

archive.org (Global: 6th place; English: 6th place)

arm.com (Global: 4,773rd place; English: 3,130th place)

developer.arm.com

arxiv.org (Global: 69th place; English: 59th place)

berkeley.edu (Global: 580th place; English: 462nd place)

cs.berkeley.edu

books.google.com (Global: 3rd place; English: 3rd place)

doi.org (Global: 2nd place; English: 2nd place)

handle.net (Global: 102nd place; English: 76th place)