Gowers 2002, p. 118 "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, ISBN978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (27 December 2012), "What is the Smallest Prime?", Journal of Integer Sequences, 15 (9), arXiv:1209.2007
books.google.com
Arnold 1919, p. 21 "By the same test zero surpasses all numbers in 'evenness.'"; Wong 1997, p. 479 "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, สืบค้นเมื่อ 11 April 2010 Wong, Samuel Shaw Ming (1997), Computational Methods in Physics and Engineering, World Scientific, ISBN981-02-3043-5
A 1980 Maryland law specifies, "(a) On even numbered calendar dates gasoline shall only be purchased by operators of vehicles bearing personalized registration plates containing no numbers and registration plates with the last digit ending in an even number. This shall not include ham radio operator plates. Zero is an even number; (b) On odd numbered calendar dates ..." Partial quotation taken from Department of Legislative Reference (1974), Laws of the State of Maryland, Volume 2, p. 3236, สืบค้นเมื่อ 2 June 2013
deseretnews.com
Sones & Sones 2002 "It follows that zero is even, and that 2/20/2000 nicely cracks the puzzle. Yet it's always surprising how much people are bothered by calling zero even..."; Column 8 readers 2006a "'...according to mathematicians, the number zero, along with negative numbers and fractions, is neither even nor odd,' writes Etan..."; Column 8 readers 2006b "'I agree that zero is even, but is Professor Bunder wise to 'prove' it by stating that 0 = 2 x 0? By that logic (from a PhD in mathematical logic, no less), as 0 = 1 x 0, it's also odd!' The prof will dispute this and, logically, he has a sound basis for doing so, but we may be wearing this topic a little thin ..." Sones, Bill; Sones, Rich (8 May 2002), "To hide your age, button your lips", Deseret News, p. C07, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2018-02-04, สืบค้นเมื่อ 21 June 2014 Column 8 readers (10 March 2006a), "Column 8", The Sydney Morning Herald (First ed.), p. 18, แม่แบบ:Factiva Column 8 readers (16 March 2006b), "Column 8", The Sydney Morning Herald (First ed.), p. 20, แม่แบบ:Factiva
Sones & Sones 2002 "Penn State mathematician George Andrews, who recalls a time of gas rationing in Australia ... Then someone in the New South Wales parliament asserted this meant plates ending in zero could never get gas, because 'zero is neither odd nor even. So the New South Wales parliament ruled that for purposes of gas rationing, zero is an even number!'" Sones, Bill; Sones, Rich (8 May 2002), "To hide your age, button your lips", Deseret News, p. C07, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2018-02-04, สืบค้นเมื่อ 21 June 2014
This is the timeframe in United States, Canada, Great Britain, Australia, and Israel; see Levenson, Tsamir & Tirosh (2007, p. 85) Levenson, Esther; Tsamir, Pessia; Tirosh, Dina (2007), "Neither even nor odd: Sixth grade students' dilemmas regarding the parity of zero", The Journal of Mathematical Behavior, 26 (2): 83–95, doi:10.1016/j.jmathb.2007.05.004
Levenson, Tsamir & Tirosh 2007, pp. 83–95 Levenson, Esther; Tsamir, Pessia; Tirosh, Dina (2007), "Neither even nor odd: Sixth grade students' dilemmas regarding the parity of zero", The Journal of Mathematical Behavior, 26 (2): 83–95, doi:10.1016/j.jmathb.2007.05.004
Hill et al. 2008, pp. 446–447. Hill, Heather C.; Blunk, Merrie L.; Charalambous, Charalambos Y.; Lewis, Jennifer M.; Phelps, Geoffrey C.; Sleep, Laurie; Ball, Deborah Loewenberg (2008), "Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study", Cognition and Instruction, 26 (4): 430–511, doi:10.1080/07370000802177235
As concluded by Levenson, Tsamir & Tirosh (2007, p. 93), referencing Freudenthal (1983, p. 460) Levenson, Esther; Tsamir, Pessia; Tirosh, Dina (2007), "Neither even nor odd: Sixth grade students' dilemmas regarding the parity of zero", The Journal of Mathematical Behavior, 26 (2): 83–95, doi:10.1016/j.jmathb.2007.05.004 Freudenthal, H. (1983), Didactical phenomenology of mathematical structures, Dordrecht, The Netherlands: Reidel
Nuerk, Iversen & Willmes (2004, p. 851): "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
Dehaene, Bossini & Giraux 1993, p. 376 "In some intuitive sense, the notion of parity is familiar only for numbers larger than 2. Indeed, before the experiment, some L subjects were unsure whether 0 was odd or even and had to be reminded of the mathematical definition. The evidence, in brief, suggests that instead of being calculated on the fly by using a criterion of divisibility by 2, parity information is retrieved from memory together with a number of other semantic properties ... If a semantic memory is accessed in parity judgments, then interindividual differences should be found depending on the familiarity of the subjects with number concepts." 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, สืบค้นเมื่อ 13 September 2007
Nuerk, Iversen & Willmes 2004, pp. 838, 860–861 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
Snow 2001; Morgan 2001 Snow, Tony (23 February 2001), "Bubba's fools", Jewish World Review, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2011-01-02, สืบค้นเมื่อ 22 August 2009 Morgan, Frank (5 April 2001), "Old Coins", Frank Morgan's Math Chat, The Mathematical Association of America, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2009-01-08, สืบค้นเมื่อ 22 August 2009
Snow 2001; Morgan 2001 Snow, Tony (23 February 2001), "Bubba's fools", Jewish World Review, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2011-01-02, สืบค้นเมื่อ 22 August 2009 Morgan, Frank (5 April 2001), "Old Coins", Frank Morgan's Math Chat, The Mathematical Association of America, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2009-01-08, สืบค้นเมื่อ 22 August 2009
Ball, Lewis & Thames (2008, p. 15) อภิปรายความท้าทายนี้สำหรับครูประถมศึกษา ผู้ต้องการให้เหตุผลทางคณิตศาสตร์แก่ข้อเท็จจริงทางคณิตศาสตร์ แต่นักเรียนไม่ใช้บทนิยามเดียวกัน หรือหากสอนแล้วจะไม่เข้าใจ 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, สืบค้นเมื่อ 4 March 2010
Ball, Lewis & Thames 2008, p. 27, Figure 1.5 "Mathematical claims about zero." 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, สืบค้นเมื่อ 4 March 2010
Ball, Lewis & Thames 2008, p. 16. 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, สืบค้นเมื่อ 4 March 2010
Ball, Lewis & Thames 2008, p. 15. See also Ball's keynote for further discussion of appropriate definitions. 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, สืบค้นเมื่อ 4 March 2010
Dehaene, Bossini & Giraux 1993, p. 376 "In some intuitive sense, the notion of parity is familiar only for numbers larger than 2. Indeed, before the experiment, some L subjects were unsure whether 0 was odd or even and had to be reminded of the mathematical definition. The evidence, in brief, suggests that instead of being calculated on the fly by using a criterion of divisibility by 2, parity information is retrieved from memory together with a number of other semantic properties ... If a semantic memory is accessed in parity judgments, then interindividual differences should be found depending on the familiarity of the subjects with number concepts." 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, สืบค้นเมื่อ 13 September 2007
Gowers 2002, p. 118 "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, ISBN978-0-19-285361-5 Caldwell, Chris K.; Xiong, Yeng (27 December 2012), "What is the Smallest Prime?", Journal of Integer Sequences, 15 (9), arXiv:1209.2007
web.archive.org
Snow 2001; Morgan 2001 Snow, Tony (23 February 2001), "Bubba's fools", Jewish World Review, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2011-01-02, สืบค้นเมื่อ 22 August 2009 Morgan, Frank (5 April 2001), "Old Coins", Frank Morgan's Math Chat, The Mathematical Association of America, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2009-01-08, สืบค้นเมื่อ 22 August 2009
Sones & Sones 2002 "It follows that zero is even, and that 2/20/2000 nicely cracks the puzzle. Yet it's always surprising how much people are bothered by calling zero even..."; Column 8 readers 2006a "'...according to mathematicians, the number zero, along with negative numbers and fractions, is neither even nor odd,' writes Etan..."; Column 8 readers 2006b "'I agree that zero is even, but is Professor Bunder wise to 'prove' it by stating that 0 = 2 x 0? By that logic (from a PhD in mathematical logic, no less), as 0 = 1 x 0, it's also odd!' The prof will dispute this and, logically, he has a sound basis for doing so, but we may be wearing this topic a little thin ..." Sones, Bill; Sones, Rich (8 May 2002), "To hide your age, button your lips", Deseret News, p. C07, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2018-02-04, สืบค้นเมื่อ 21 June 2014 Column 8 readers (10 March 2006a), "Column 8", The Sydney Morning Herald (First ed.), p. 18, แม่แบบ:Factiva Column 8 readers (16 March 2006b), "Column 8", The Sydney Morning Herald (First ed.), p. 20, แม่แบบ:Factiva
Sones & Sones 2002 "Penn State mathematician George Andrews, who recalls a time of gas rationing in Australia ... Then someone in the New South Wales parliament asserted this meant plates ending in zero could never get gas, because 'zero is neither odd nor even. So the New South Wales parliament ruled that for purposes of gas rationing, zero is an even number!'" Sones, Bill; Sones, Rich (8 May 2002), "To hide your age, button your lips", Deseret News, p. C07, คลังข้อมูลเก่าเก็บจากแหล่งเดิมเมื่อ 2018-02-04, สืบค้นเมื่อ 21 June 2014
