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==Bibliography== {{refbegin|25em|small=yes}} * {{cite book |last=Bluman |first=Allan |year=2010 |edition=Second |title=Pre-Algebra DeMYSTiFieD |publisher=McGraw-Hill Professional |isbn=978-0-07-174251-1 |url=https://books.google.com/books?id=oRLc9r4bmSgC |via=Google Books }} * {{cite book |last=Carothers |first=N.L. |year=2000 |title=Real Analysis |publisher=Cambridge University Press |isbn=978-0-521-49756-5 |via=Google Books |url=https://books.google.com/books?id=4VFDVy1NFiAC&q=%22natural+numbers%22 }} * {{cite book |last1=Clapham |first1=Christopher |last2=Nicholson |first2=James |year=2014 |edition=Fifth |title=The Concise Oxford Dictionary of Mathematics |publisher=Oxford University Press |isbn=978-0-19-967959-1 |via=Google Books |url=https://books.google.com/books?id=c69GBAAAQBAJ }} * {{cite book |last=Dedekind |first=Richard |author-link=Richard Dedekind |translator-last=Beman |translator-first=Wooster Woodruff |orig-year=1901 |year=1963 |edition=reprint |title=Essays on the Theory of Numbers |publisher=Dover Books |isbn=978-0-486-21010-0 |via=Archive.org |url=https://archive.org/details/essaysontheoryof0000dede }} ** {{cite book |author-first=Richard |author-last=Dedekind |author-link=Richard Dedekind |translator-first=Wooster Woodruff |translator-last=Beman |year=1901 |title=Essays on the Theory of Numbers |publisher=Open Court Publishing Company |place=Chicago, IL |via=Project Gutenberg |url=https://www.gutenberg.org/ebooks/21016 |access-date=13 August 2020 }} ** {{cite book |last=Dedekind |first=Richard |author-link=Richard Dedekind |orig-year=1901 |year=2007 |title=Essays on the Theory of Numbers |publisher=Kessinger Publishing, LLC |isbn=978-0-548-08985-9 }} * {{cite book |last=Eves |first=Howard |author-link=Howard Eves |year=1990 |edition=6th |title=An Introduction to the History of Mathematics |publisher=Thomson |isbn=978-0-03-029558-4 |via=Google Books |url=https://books.google.com/books?id=PXvwAAAAMAAJ }} * {{cite book |last=Halmos |first=Paul |author-link=Paul Halmos |year=1960 |title=Naive Set Theory |publisher=Springer Science & Business Media |isbn=978-0-387-90092-6 |via=Google Books |url=https://books.google.com/books?id=x6cZBQ9qtgoC&q=peano+axioms&pg=PP1 }} * {{cite book |last=Hamilton |first=A.G. |year=1988 |edition=Revised |title=Logic for Mathematicians |publisher=Cambridge University Press |isbn=978-0-521-36865-0 |via=Google Books |url=https://books.google.com/books?id=TO098EjWT38C&q=peano%27s+postulates }} * {{cite book |last1=James |first1=Robert C. |author-link1=Robert C. James |last2=James |first2=Glenn |year=1992 |edition=Fifth |title=Mathematics Dictionary |publisher=Chapman & Hall |isbn=978-0-412-99041-0 |via=Google Books |url=https://books.google.com/books?id=UyIfgBIwLMQC }} * {{cite book |last=Landau |first=Edmund |author-link=Edmund Landau |year=1966 |edition=Third |title=Foundations of Analysis |publisher=Chelsea Publishing |isbn=978-0-8218-2693-5 |via=Google Books |url=https://books.google.com/books?id=DvIJBAAAQBAJ }} * {{cite book |last=Levy |first=Azriel |author-link=Azriel Levy |year=1979 |title=Basic Set Theory |publisher=Springer-Verlag Berlin Heidelberg |isbn= 978-3-662-02310-5 }} * {{cite book |last1=Mac Lane |first1=Saunders |author1-link=Saunders Mac Lane |last2=Birkhoff |first2=Garrett |author2-link=Garrett Birkhoff |year=1999 |edition=3rd |title=Algebra |publisher=American Mathematical Society |isbn=978-0-8218-1646-2 |via=Google Books |url=https://books.google.com/books?id=L6FENd8GHIUC&q=%22the+natural+numbers%22&pg=PA15 }} * {{cite book |last=Mendelson |first=Elliott |author-link=Elliott Mendelson |orig-year=1973 |year=2008 |title=Number Systems and the Foundations of Analysis |publisher=Dover Publications |isbn=978-0-486-45792-5 |via=Google Books |url=https://books.google.com/books?id=3domViIV7HMC }} * {{cite book |last=Morash |first=Ronald P. |year=1991 |edition=Second |title=Bridge to Abstract Mathematics: Mathematical proof and structures |publisher=Mcgraw-Hill College |isbn=978-0-07-043043-3 |via=Google Books |url=https://books.google.com/books?id=fH9YAAAAYAAJ }} * {{cite book |last1=Musser |first1=Gary L. |last2=Peterson |first2=Blake E. |last3=Burger |first3=William F. |year=2013 |edition=10th |title=Mathematics for Elementary Teachers: A contemporary approach |publisher=[[Wiley Global Education]] |isbn=978-1-118-45744-3 |via=Google Books |url=https://books.google.com/books?id=b3dbAgAAQBAJ }} * {{cite book |last1=Szczepanski |first1=Amy F. |last2=Kositsky |first2=Andrew P. |year=2008 |title=The Complete Idiot's Guide to Pre-algebra |publisher=Penguin Group |isbn=978-1-59257-772-9 |via=Google Books |url=https://books.google.com/books?id=wLA2tlR_LYYC }} * {{cite book |last1=Thomson |first1=Brian S. |last2=Bruckner |first2=Judith B. |last3=Bruckner |first3=Andrew M. |year=2008 |edition=Second |title=Elementary Real Analysis |publisher=ClassicalRealAnalysis.com |isbn=978-1-4348-4367-8 |via=Google Books |url=https://books.google.com/books?id=vA9d57GxCKgC }} * {{cite journal |last=von Neumann |first=John |author-link=John von Neumann |year=1923 |title=Zur Einführung der transfiniten Zahlen |trans-title=On the Introduction of the Transfinite Numbers |journal=Acta Litterarum AC Scientiarum Ragiae Universitatis Hungaricae Francisco-Josephinae, Sectio Scientiarum Mathematicarum |volume=1 |pages=199–208 |url=http://acta.fyx.hu/acta/showCustomerArticle.action?id=4981&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=39716d660ae98d02&style= |url-status=dead |access-date=15 September 2013 |archive-url=https://web.archive.org/web/20141218090535/http://acta.fyx.hu/acta/showCustomerArticle.action?id=4981&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=39716d660ae98d02&style= |archive-date=18 December 2014 }} * {{cite book |author-last=von Neumann |author-first=John |author-link=John von Neumann |editor-first=Jean |editor-last=van Heijenoort |orig-year=1923 |date=January 2002 |edition=3rd |title=From Frege to Gödel: A source book in mathematical logic, 1879–1931 |chapter=On the introduction of transfinite numbers |pages=346–354 |isbn=978-0-674-32449-7 |publisher=Harvard University Press |chapter-url=http://www.hup.harvard.edu/catalog.php?isbn=978-0674324497 }} – English translation of {{Harvnb|von Neumann|1923}}. {{refend}}
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