0의 홀짝성 (Korean Wikipedia)

Analysis of information sources in references of the Wikipedia article "0의 홀짝성" in Korean language version.

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23wikipedia.org

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archive.org

Penner 1999, 34쪽: Lemma B.2.2, The integer 0 is even and is not odd. Penner uses the mathematical symbol ∃, the existential quantifier, to state the proof: "To see that 0 is even, we must prove that ∃k (0 = 2k), and this follows from the equality 0 = 2 ⋅ 0." Penner, Robert C. (1999), 《Discrete Mathematics: Proof Techniques and Mathematical Structures》, River Edje: World Scientific, ISBN 978-981-02-4088-2
Penner 1999, 34쪽. Penner, Robert C. (1999), 《Discrete Mathematics: Proof Techniques and Mathematical Structures》, River Edje: World Scientific, ISBN 978-981-02-4088-2
Salzmann 등. 2007, 168쪽 Salzmann, H.; Grundhöfer, T.; Hähl, H.; Löwen, R. (2007), 《The Classical Fields: Structural Features of the Real and Rational Numbers》, Cambridge University Press, ISBN 978-0-521-86516-6

arxiv.org

Caldwell & Xiong 2012, 5–6쪽. Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C
Gowers 2002, 118쪽 "The seemingly arbitrary exclusion of 1 from the definition of a prime … does not express some deep fact about numbers: it just happens to be a useful convention, adopted so there is only one way of factorizing any given number into primes." For a more detailed discussion, see Caldwell & Xiong (2012). Gowers, Timothy (2002), 《Mathematics: A Very Short Introduction》, Oxford University Press, ISBN 978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C

books.google.com

Arnold 1919, 21쪽 "By the same test zero surpasses all numbers in 'evenness.'"; Wong 1997, 479쪽 "Thus, the integer b000⋯000 = 0 is the most 'even.' Arnold, C. L. (January 1919), “The Number Zero”, 《The Ohio Educational Monthly》 68 (1): 21–22, 2010년 4월 11일에 확인함 Wong, Samuel Shaw Ming (1997), 《Computational Methods in Physics and Engineering》, World Scientific, ISBN 978-981-02-3043-2

diva-portal.org

Dickerson & Pitman 2012, 191쪽. Dickerson, David S; Pitman, Damien J (July 2012), Tai-Yih Tso, 편집., “Advanced college-level students' categorization and use of mathematical definitions” (PDF), 《Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education》 2: 187–195

doi.org

dx.doi.org

Compare Lichtenberg (1972, 535쪽) Fig. 1 Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 535–536쪽 "...numbers answer the question How many? for the set of objects ... zero is the number property of the empty set ... If the elements of each set are marked off in groups of two ... then the number of that set is an even number." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 535–536쪽 "Zero groups of two stars are circled. No stars are left. Therefore, zero is an even number." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 537쪽; compare her Fig. 3. "If the even numbers are identified in some special way ... there is no reason at all to omit zero from the pattern." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 537–538쪽 "At a more advanced level ... numbers expressed as (2 × ▢) + 0 are even numbers ... zero fits nicely into this pattern." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lorentz 1994, 5–6쪽; Lovas & Pfenning 2008, 115쪽; Nipkow, Paulson & Wenzel 2002, 127쪽 Lorentz, Richard J. (1994), 《Recursive Algorithms》, Intellect Books, ISBN 978-1-56750-037-0 Lovas, William; Pfenning, Frank (2008년 1월 22일), “A Bidirectional Refinement Type System for LF”, 《Electronic Notes in Theoretical Computer Science》 196: 113–128, doi:10.1016/j.entcs.2007.09.021 Nipkow, Tobias; Paulson, Lawrence C.; Wenzel, Markus (2002), 《Isabelle/Hol: A Proof Assistant for Higher-Order Logic》, Springer, ISBN 978-3-540-43376-7
Nuerk, Iversen & Willmes (2004, 851쪽): "It can also be seen that zero strongly differs from all other numbers regardless of whether it is responded to with the left or the right hand. (See the line that separates zero from the other numbers.)" Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272
See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272

harvard.edu

adsabs.harvard.edu

Caldwell & Xiong 2012, 5–6쪽. Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C
Gowers 2002, 118쪽 "The seemingly arbitrary exclusion of 1 from the definition of a prime … does not express some deep fact about numbers: it just happens to be a useful convention, adopted so there is only one way of factorizing any given number into primes." For a more detailed discussion, see Caldwell & Xiong (2012). Gowers, Timothy (2002), 《Mathematics: A Very Short Introduction》, Oxford University Press, ISBN 978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C

nih.gov

ncbi.nlm.nih.gov

Nuerk, Iversen & Willmes (2004, 851쪽): "It can also be seen that zero strongly differs from all other numbers regardless of whether it is responded to with the left or the right hand. (See the line that separates zero from the other numbers.)" Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272
See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272

semanticscholar.org

api.semanticscholar.org

Nuerk, Iversen & Willmes (2004, 851쪽): "It can also be seen that zero strongly differs from all other numbers regardless of whether it is responded to with the left or the right hand. (See the line that separates zero from the other numbers.)" Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272
See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272

umich.edu

www-personal.umich.edu

Ball, Lewis & Thames (2008, 15쪽) discuss this challenge for the elementary-grades teacher, who wants to give mathematical reasons for mathematical facts, but whose students neither use the same definition, nor would understand it if it were introduced. Ball, Deborah Loewenberg; Lewis, Jennifer; Thames, Mark Hoover (2008), “Making mathematics work in school” (PDF), 《Journal for Research in Mathematics Education》 M14: 13–44 and 195–200, 2010년 3월 4일에 확인함

unicog.org

See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272

uwaterloo.ca

cs.uwaterloo.ca

Caldwell & Xiong 2012, 5–6쪽. Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C
Gowers 2002, 118쪽 "The seemingly arbitrary exclusion of 1 from the definition of a prime … does not express some deep fact about numbers: it just happens to be a useful convention, adopted so there is only one way of factorizing any given number into primes." For a more detailed discussion, see Caldwell & Xiong (2012). Gowers, Timothy (2002), 《Mathematics: A Very Short Introduction》, Oxford University Press, ISBN 978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C

web.archive.org

See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272

wikipedia.org

en.wikipedia.org

Arnold 1919, 21쪽 "By the same test zero surpasses all numbers in 'evenness.'"; Wong 1997, 479쪽 "Thus, the integer b000⋯000 = 0 is the most 'even.' Arnold, C. L. (January 1919), “The Number Zero”, 《The Ohio Educational Monthly》 68 (1): 21–22, 2010년 4월 11일에 확인함 Wong, Samuel Shaw Ming (1997), 《Computational Methods in Physics and Engineering》, World Scientific, ISBN 978-981-02-3043-2
Penner 1999, 34쪽: Lemma B.2.2, The integer 0 is even and is not odd. Penner uses the mathematical symbol ∃, the existential quantifier, to state the proof: "To see that 0 is even, we must prove that ∃k (0 = 2k), and this follows from the equality 0 = 2 ⋅ 0." Penner, Robert C. (1999), 《Discrete Mathematics: Proof Techniques and Mathematical Structures》, River Edje: World Scientific, ISBN 978-981-02-4088-2
Ball, Lewis & Thames (2008, 15쪽) discuss this challenge for the elementary-grades teacher, who wants to give mathematical reasons for mathematical facts, but whose students neither use the same definition, nor would understand it if it were introduced. Ball, Deborah Loewenberg; Lewis, Jennifer; Thames, Mark Hoover (2008), “Making mathematics work in school” (PDF), 《Journal for Research in Mathematics Education》 M14: 13–44 and 195–200, 2010년 3월 4일에 확인함
Compare Lichtenberg (1972, 535쪽) Fig. 1 Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 535–536쪽 "...numbers answer the question How many? for the set of objects ... zero is the number property of the empty set ... If the elements of each set are marked off in groups of two ... then the number of that set is an even number." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 535–536쪽 "Zero groups of two stars are circled. No stars are left. Therefore, zero is an even number." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Dickerson & Pitman 2012, 191쪽. Dickerson, David S; Pitman, Damien J (July 2012), Tai-Yih Tso, 편집., “Advanced college-level students' categorization and use of mathematical definitions” (PDF), 《Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education》 2: 187–195
Lichtenberg 1972, 537쪽; compare her Fig. 3. "If the even numbers are identified in some special way ... there is no reason at all to omit zero from the pattern." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Lichtenberg 1972, 537–538쪽 "At a more advanced level ... numbers expressed as (2 × ▢) + 0 are even numbers ... zero fits nicely into this pattern." Lichtenberg, Betty Plunkett (November 1972), “Zero is an even number”, 《The Arithmetic Teacher》 19 (7): 535–538, doi:10.5951/AT.19.7.0535
Caldwell & Xiong 2012, 5–6쪽. Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C
Gowers 2002, 118쪽 "The seemingly arbitrary exclusion of 1 from the definition of a prime … does not express some deep fact about numbers: it just happens to be a useful convention, adopted so there is only one way of factorizing any given number into primes." For a more detailed discussion, see Caldwell & Xiong (2012). Gowers, Timothy (2002), 《Mathematics: A Very Short Introduction》, Oxford University Press, ISBN 978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (2012년 12월 27일), “What is the Smallest Prime?”, 《Journal of Integer Sequences》 15 (9), arXiv:1209.2007, Bibcode:2012arXiv1209.2007C
Partee 1978, xxi쪽 Partee, Barbara Hall (1978), 《Fundamentals of Mathematics for Linguistics》, Dordrecht: D. Reidel, ISBN 978-90-277-0809-0
Stewart 2001, 54쪽 These rules are given, but they are not quoted verbatim. Stewart, Mark Alan (2001), 《30 Days to the GMAT CAT》, Stamford: Thomson, ISBN 978-0-7689-0635-6
Devlin 1985, 30–33쪽 Devlin, Keith (April 1985), “The golden age of mathematics”, 《New Scientist》 106 (1452)
Penner 1999, 34쪽. Penner, Robert C. (1999), 《Discrete Mathematics: Proof Techniques and Mathematical Structures》, River Edje: World Scientific, ISBN 978-981-02-4088-2
Berlinghoff, Grant & Skrien 2001 For isolated vertices see p. 149; for groups see p. 311. Berlinghoff, William P.; Grant, Kerry E.; Skrien, Dale (2001), 《A Mathematics Sampler: Topics for the Liberal Arts》 5 rev.판, Rowman & Littlefield, ISBN 978-0-7425-0202-4
Lovász, Pelikán & Vesztergombi 2003, 127–128쪽 Lovász, László; Pelikán, József; Vesztergombi, Katalin L. (2003), 《Discrete Mathematics: Elementary and Beyond》, Springer, ISBN 978-0-387-95585-8
Lorentz 1994, 5–6쪽; Lovas & Pfenning 2008, 115쪽; Nipkow, Paulson & Wenzel 2002, 127쪽 Lorentz, Richard J. (1994), 《Recursive Algorithms》, Intellect Books, ISBN 978-1-56750-037-0 Lovas, William; Pfenning, Frank (2008년 1월 22일), “A Bidirectional Refinement Type System for LF”, 《Electronic Notes in Theoretical Computer Science》 196: 113–128, doi:10.1016/j.entcs.2007.09.021 Nipkow, Tobias; Paulson, Lawrence C.; Wenzel, Markus (2002), 《Isabelle/Hol: A Proof Assistant for Higher-Order Logic》, Springer, ISBN 978-3-540-43376-7
Bunch 1982, 165쪽 Bunch, Bryan H. (1982), 《Mathematical Fallacies and Paradoxes》, Van Nostrand Reinhold, ISBN 978-0-442-24905-2
Salzmann 등. 2007, 168쪽 Salzmann, H.; Grundhöfer, T.; Hähl, H.; Löwen, R. (2007), 《The Classical Fields: Structural Features of the Real and Rational Numbers》, Cambridge University Press, ISBN 978-0-521-86516-6
Wise 2002, 66–67쪽 Wise, Stephen (2002), 《GIS Basics》, CRC Press, ISBN 978-0-415-24651-4
Nuerk, Iversen & Willmes (2004, 851쪽): "It can also be seen that zero strongly differs from all other numbers regardless of whether it is responded to with the left or the right hand. (See the line that separates zero from the other numbers.)" Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272
See data throughout Dehaene, Bossini & Giraux (1993), and summary by Nuerk, Iversen & Willmes (2004, 837쪽). Dehaene, Stanislas; Bossini, Serge; Giraux, Pascal (1993), “The mental representation of parity and numerical magnitude” (PDF), 《Journal of Experimental Psychology: General》 122 (3): 371–396, doi:10.1037/0096-3445.122.3.371, 2011년 7월 19일에 원본 문서 (PDF)에서 보존된 문서, 2007년 9월 13일에 확인함 Nuerk, Hans-Christoph; Iversen, Wiebke; Willmes, Klaus (July 2004), “Notational modulation of the SNARC and the MARC (linguistic markedness of response codes) effect”, 《The Quarterly Journal of Experimental Psychology A》 57 (5): 835–863, doi:10.1080/02724980343000512, PMID 15204120, S2CID 10672272