Editing Addition (section)

== References ==
{{refbegin|30em}}
* {{cite journal
 | last1 = Akian | first1 = Marianne
 | last2 = Bapat | first2 = Ravindra
 | last3 = Gaubert | first3 = Stephane
 | title = Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem
 | journal = INRIA Reports
 | year = 2005
 | arxiv = math.SP/0402090
 | bibcode = 2004math......2090A
}}
* {{cite book
 | last = Apostol | first = Tom M.
 | title = Calculus
 | year = 1967
 | publisher = [[John Wiley & Sons]]
 | edition = 2nd
 | volume = 1
}}
* {{cite conference
 | last1 = Baez | first1 = J. | author-link1 = John C. Baez
 | last2 = Dolan | first2 = J.
 | book-title = Mathematics Unlimited – 2001 and Beyond. From Finite Sets to Feynman Diagrams
 | year = 2001
 | page = 29
 | arxiv = math.QA/0004133
 | isbn = 3-540-66913-2
}}
* {{cite book
 | last = Begle | first = Edward
 | title = The Mathematics of the Elementary School
 | publisher = [[McGraw-Hill]]
 | year = 1975
 | isbn = 978-0-07-004325-1
 | url = https://archive.org/details/mathematicsofele0000begl
}}
* {{cite book
 | last = Berg | first = Lothar
 | editor-last1 = Lauwerier | editor-first1 = H. A.
 | editor-last2 = Koiter | editor-first2 = W. T.
 | title = Introduction To The Operational Calculus
 | url = https://books.google.com/books?id=aGXFCUaFCW0C
 | publisher = North-Holland Publishing
 | volume = 2
 | year = 1967
| isbn = 978-0-323-16245-6
 }}
* {{cite book
 | last = Bergman | first = George
 | title = An Invitation to General Algebra and Universal Constructions
 | edition = 2.3
 | publisher = General Printing
 | year = 2005
 | isbn = 978-0-9655211-4-7
 | url = http://math.berkeley.edu/~gbergman/245/index.html
}}
* {{cite book
 | last1 = Behr | first1 = Merlyn J.
 | last2 = Jungst | first2 = Dale G.
 | title = Fundamentals of Elementary Mathematics
 | year = 1971
 | publisher = Academic Press
}}
* {{cite book
 | last1 = Bronstein | first1 = Ilja Nikolaevič
 | last2 = Semendjajew | first2 = Konstantin Adolfovič
 | editor1-first = Günter | editor1-last = Grosche
 | editor2-first = Viktor | editor2-last = Ziegler
 | editor3-first = Dorothea | editor3-last = Ziegler
 | others = Weiß, Jürgen
 | translator-first = Viktor | translator-last = Ziegler
 | volume = 1 | year = 1987 | edition = 23
 | orig-year = 1945 | publisher = [[Verlag Harri Deutsch]] (and [[B.G. Teubner Verlagsgesellschaft]], Leipzig)
 | location = Thun and Frankfurt am Main
 | language = de
 | chapter = 2.4.1.1.
 | pages = 115–120
 | isbn = 978-3-87144-492-0
 | title = Taschenbuch der Mathematik
 | title-link = Bronstein and Semendjajew
}}
* {{cite book
 | last = Burrill | first = Claude
 | title = Foundations of Real Numbers
 | publisher = McGraw-Hill
 | year = 1967
 | id = {{LCC|QA248.B95}}
}}
* {{cite web |last=Bogomolny |first=Alexander |year=1996 |title=Addition |work=Interactive Mathematics Miscellany and Puzzles (cut-the-knot.org) |url=http://www.cut-the-knot.org/do_you_know/addition.shtml |access-date=3 February 2006 |archive-url=https://web.archive.org/web/20060426110928/http://www.cut-the-knot.org/do_you_know/addition.shtml |archive-date=April 26, 2006 |url-status=live}}
* {{cite book
 | last1 = Cameron | first1 = Scyhrlet
 | last2 = Craig | first2 = Carolyn 
 | year = 2013
 | title = Adding and Subtracting Fractions, Grades 5–8
 | publisher = Mark Twain Incorporation
}}
* {{cite book
 | last = Campbell | first = Howard E.
 | title = The structure of arithmetic
 | publisher = Appleton-Century-Crofts
 | year = 1970
 | isbn = 978-0-390-16895-5
 | url-access = registration
 | url = https://archive.org/details/structureofarith00camp}}
* {{cite book
 | last = Cheng | first = Eugenia | author-link = Eugenia Cheng
 | title = Beyond Infinity: An Expedition to the Outer Limits of Mathematics
 | title-link = Beyond Infinity (mathematics book)
 | year = 2017
 | publisher = Basic Books
 | isbn = 978-1-541-64413-7
}}
* {{cite book
 | author = Department of the Army
 | year = 1961
 | title = Army Technical Manual TM 11-684: Principles and Applications of Mathematics for Communications-Electronics
}}
* {{cite book
 | last1 = Devine | first1 = D.
 | last2 = Olson | first2 = J.
 | last3 = Olson | first3 = M.
 | title = Elementary Mathematics for Teachers
 | edition = 2e
 | publisher = [[John Wiley & Sons]]
 | year = 1991
 | isbn = 978-0-471-85947-5
 | url = https://archive.org/details/elementarymathem0000devi
}}
* {{cite book
 | last1 = Dummit | first1 = D.
 | last2 = Foote | first2 = R.
 | title = Abstract Algebra
 | edition = 2nd
 | publisher = Wiley
 | year = 1999
 | isbn = 978-0-471-36857-1
}}
* {{cite book
 | last = Dunham | first = William
 | title = The Mathematical Universe
 | url = https://archive.org/details/mathematicaluniv0000dunh
 | url-access = registration
 | publisher = Wiley
 | year = 1994
 | isbn = 978-0-471-53656-7
}}
* {{cite book
 | last = Enderton | first = Herbert
 | title = Elements of Set Theory
 | publisher = [[Academic Press]]
 | year = 1977
 | isbn = 978-0-12-238440-0
 | url = https://books.google.com/books?id=JlR-Ehk35XkC
}}
* {{cite book
 | last = Ferreirós | first = José
 | title = Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics 
 | url = https://archive.org/details/labyrinthofthoug0000ferr
 | url-access = registration
 | publisher = Birkhäuser
 | year = 1999
 | isbn = 978-0-8176-5749-9
}}
* {{cite book
 | last = Fierro | first = R.
 | year = 2012
 | title = Mathematics for Elementary School Teachers
 | publisher = Cengage Learning
}}
* {{cite book
 | last1 = Flynn | first1 = M.
 | last2 = Oberman | first2 = S.
 | title = Advanced Computer Arithmetic Design
 | publisher = Wiley
 | year = 2001
 | isbn = 978-0-471-41209-0
}}
* {{cite book
 | last1 = Fosnot | first1 = Catherine T.
 | last2 = Dolk | first2 = Maarten
 | title = Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction
 | publisher = Heinemann
 | year = 2001
 | isbn = 978-0-325-00353-5
}}
* {{cite book
 | last = Gbur | first = Greg | author-link = Greg Gbur
 | url = https://www.worldcat.org/oclc/704518582
 | title = Mathematical Methods for Optical Physics and Engineering
 | year = 2011
 | publisher = [[Cambridge University Press]]
 | isbn = 978-0-511-91510-9
 | oclc = 704518582
}}
* {{cite book
 | last1 = Gschwind | first1 = Hans W.
 | last2 = McCluskey | first2 = E. J.
 | year = 1975
 | title = Design of Digital Computers: An Introduction
 | publisher = Springer-Verlag
 | edition = 2nd
}}
* {{cite book
 | last = Hempel | first = C. G.
 | editor-last = Fetzer | editor-first = J. H.
 | year = 2001
 | title = The philosophy of Carl G. Hempel: studies in science, explanation, and rationality
 | url = https://books.google.com/books?id=yTY9La4P2n8C
 | publisher = Oxford University Press
| isbn = 978-0-19-534387-8
 }}
* {{cite book
 | last1 = Horowitz | first1 = P.
 | last2 = Hill | first2 = W.
 | title = The Art of Electronics
 | edition = 2nd
 | publisher = Cambridge University Press
 | year = 2001
 | isbn = 978-0-521-37095-0
 | url = https://archive.org/details/artofelectronics00horo
}}
* {{cite book
 | last = Jackson | first = Albert
 | title = Analog Computation
 | publisher = McGraw-Hill
 | year = 1960
 | id = {{LCC|QA76.4|J3}}
}}
* {{cite book
 | last = Johnson | first = Paul
 | title = From Sticks and Stones: Personal Adventures in Mathematics
 | publisher = Science Research Associates
 | year = 1975
 | isbn = 978-0-574-19115-1
}}
* {{cite book
 | last = Kaplan | first = Robert
 | title = The Nothing That Is: A Natural History of Zero
 | publisher = [[Oxford University Press]]
 | year = 2000
 | isbn = 0-19-512842-7
}}
* {{cite book
 | last = Karpinski | first = Louis | author-link = Louis Charles Karpinski
 | title = The History of Arithmetic
 | publisher = Rand McNally
 | year = 1925
 | id = {{LCC|QA21.K3}}
}}
* {{cite book
 | last = Kay | first = Anthony
 | title = Number Systems: A Path into Rigorous Mathematics
 | year = 2021
 | publisher = [[CRC Press]]
 | isbn = 978-0-429-60776-9
 | url = https://books.google.com/books?id=aw81EAAAQBAJ
 | language = en
}}
* {{cite book
 | last = Lee | first = John
 | title= Introduction to Smooth Manifolds
 | publisher = Springer
 | year = 2003
 | isbn = 978-0-387-95448-6
}}
* {{cite book
 | last = Lewis | first = Rhys
 | url = https://link.springer.com/book/10.1007/978-1-349-02405-6
 | title = First-Year Technician Mathematics
 | publisher = The MacMillan Press Ltd
 | year = 1974
 | isbn = 978-1-349-02405-6
 | location= Palgrave, London
 | page = 1
 | chapter = Arithmetic
 | doi = 10.1007/978-1-349-02405-6_1
 | chapter-url = https://link.springer.com/chapter/10.1007/978-1-349-02405-6_1
}}
* {{cite book
 | last1 = Li | first1 = Y.
 | last2 = Lappan | first2 = G. | author-link2 = Glenda Lappan
 | year = 2014
 | title = Mathematics curriculum in school education
 | publisher = Springer
 | doi = 10.1007/978-94-007-7560-2
 | isbn = 978-94-007-7560-2
}}
* {{cite book
 | last = Linderholm | first = Carl
 | year = 1971
 | title = Mathematics Made Difficult
 | title-link = Mathematics Made Difficult
 | publisher = Wolfe
 | isbn = 978-0-7234-0415-6
}}
* {{cite arXiv
 | last1 = Litvinov | first1 = Grigory
 | last2 = Maslov | first2 = Victor
 | last3 = Sobolevskii | first3 = Andreii
 | year = 1999
 | eprint = math/9911126
 | title = Idempotent mathematics and interval analysis
}}
* {{cite book
 | last1 = Liu | first1 = Feng
 | last2 = Tan | first2 = Qingping
 | last3 = Song | first3 = Xiaoyu
 | last4 = Chen | first4 = Gang
 | editor-last1 = Hsu | editor-first1 = Ching-Hsien
 | editor-last2 = Yang | editor-first2 = Laurence T.
 | editor-last3 = Park | editor-first3 = Jong Hyuk
 | editor-last4 = Yeo | editor-first4 = Sang-Soo
 | title = Algorithms and Architectures for Parallel Processing: 10th International Conference, ICA3PP 2010, Busan, Korea, May 21–23, 2010. Proceedings, Vol. 1
 | year = 2010
 | publisher = Springer
}}
* {{cite journal
 | last = Loday | first = Jean-Louis
 | title = Arithmetree
 | journal = Journal of Algebra
 | year = 2002
 | arxiv = math/0112034
 | doi = 10.1016/S0021-8693(02)00510-0
 | volume = 258 | page= 275
}}
* {{cite book
 | last = Marguin | first = Jean
 | year = 1994
 | language = fr
 | title = Histoire des Instruments et Machines à Calculer, Trois Siècles de Mécanique Pensante 1642–1942
 | publisher = Hermann
 | isbn = 978-2-7056-6166-3
}}
* {{cite book
 | last = Martin | first = John
 | title= Introduction to Languages and the Theory of Computation
 | publisher = McGraw-Hill
 | edition = 3rd
 | year = 2003
 | isbn= 978-0-07-232200-2
}}
* {{cite book
 | last = Mazur | first = Joseph
 | year = 2014
 | title = Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers
 | publisher = [[Princeton University Press]]
 | doi = 10.2307/j.ctt5hhpnp
 | jstor = j.ctt5hhpnp
| isbn = 978-0-691-15463-3
 }}
* {{cite book
 | last = Mikhalkin | first = Grigory
 | year = 2006
 | arxiv = math.AG/0601041
 | zbl = 1103.14034
 | editor-last = Sanz-Solé | editor-first = Marta
 | title = Proceedings of the International Congress of Mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume II: Invited lectures. Tropical Geometry and its Applications
 | location = Zürich
 | publisher = [[European Mathematical Society]]
 | isbn= 978-3-03719-022-7
 | pages = 827–852}}
* {{cite book
 | last = Mosley | first = F.
 | year = 2001
 | title = Using number lines with 5–8 year olds
 | volume = 4
 | publisher = Nelson Thornes
 | isbn = 978-1-874099-95-6
 | url = https://books.google.com/books?id=I-__WcWjemUC
}}
* {{cite book
 | last1 = Musser | first1 = Gary L.
 | last2 = Peterson | first2 = Blake E.
 | last3 = Burger | first3 = William F.
 | title = Mathematics for Elementary Teachers: A Contemporary Approach
 | year = 2013
 | publisher = [[John Wiley & Sons]]
 | isbn = 978-1-118-48700-6
 | url = https://books.google.com/books?id=8jh7DwAAQBAJ
 | language = en
}}
* {{cite book
 | author = National Research Council
 | title = Adding It Up: Helping Children Learn Mathematics
 | publisher = [[United States National Academies|National Academy Press]]
 | year = 2001
 | isbn = 978-0-309-06995-3|author-link=United States National Research Council 
 | url = http://www.nap.edu/books/0309069955/html/index.html|doi=10.17226/9822
}}
* {{cite journal
 | last = Neumann | first = Peter G.
 | url = http://catless.ncl.ac.uk/Risks/4.45.html
 | title = The Risks Digest Volume 4: Issue 45
 | journal = The Risks Digest
 | access-date = 2015-03-30
 | archive-url = https://web.archive.org/web/20141228211038/http://catless.ncl.ac.uk/Risks/4.45.html
 | archive-date = 2014-12-28
 | url-status = live
 | date = 2 February 1987
 | volume = 4 | issue = 45
}}
* {{cite book
 | last1 = Posamentier | first1 = Alfred S.
 | last2 = Farber | first2 = William
 | last3 = Germain-Williams | first3 = Terri L.
 | last4 = Paris | first4 = Elaine
 | last5 = Thaller | first5 = Bernd
 | last6 = Lehmann | first6 = Ingmar
 | year = 2013
 | title = 100 Commonly Asked Questions in Math Class
 | publisher = Corwin Press
 | isbn = 978-1-4522-4308-5
}}
* {{cite book
 | last1 = Rieffel | first1 = Eleanor G. | author-link1 = Eleanor Rieffel
 | last2 = Polak | first2 = Wolfgang H.
 | title-link = Quantum Computing: A Gentle Introduction
 | title = Quantum Computing: A Gentle Introduction
 | date = 4 March 2011
 | publisher = MIT Press
 | isbn = 978-0-262-01506-6
 | language = en
}}
* {{cite book |last=Riehl |first=Emily |author-link=Emily Riehl |title=Category Theory in Context |publisher=Dover |url=https://math.jhu.edu/~eriehl/context/ |year=2016 |isbn=978-0-486-80903-8}}
* {{cite book
 | last = Rudin | first = Walter
 | title = Principles of Mathematical Analysis
 | url = https://archive.org/details/principlesofmath00rudi
 | url-access = registration
 | edition = 3rd
 | publisher = McGraw-Hill
 | year = 1976
 | isbn = 978-0-07-054235-8
}}
* {{cite book
 | last = Rosen | first = Kenneth
 | year = 2013
 | title = Discrete Maths and Its Applications Global Edition
 | publisher = McGraw Hill
 | isbn = 978-0-07-131501-2
}}
* {{cite book
 | last = Schmid | first = Hermann | author-link = Hermann Schmid (computer scientist)
 | title = Decimal Computation
 | year = 1974
 | edition = 1st
 | publisher = [[John Wiley & Sons]]
 | location = Binghamton, NY
 | isbn = 0-471-76180-X
 | url = https://archive.org/details/decimalcomputati0000schm
}}
* {{cite book
 | last = Schmid | first = Hermann |author-link = Hermann Schmid (computer scientist)
 | title = Decimal Computation
 | orig-year = 1974 | year = 1983
 | edition = reprint of 1st
 | publisher = Robert E. Krieger Publishing Company
 | location = Malabar, FL
 | isbn = 978-0-89874-318-0
}}
* {{cite journal
 | last1 = Schmidt | first1 = W.
 | last2 = Houang | first2 = R.
 | last3 = Cogan | first3 = L.
 | year = 2002
 | title = A coherent curriculum
 | journal = American Educator
 | volume = 26 | issue = 2 | pages = 10&ndash;26
}}
* {{cite book
 | last = Schwartzman | first = Steven
 |title=The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English |url=https://archive.org/details/wordsofmathemati0000schw |url-access=registration |publisher=[[Mathematical Association of America|MAA]] |year=1994 |isbn=978-0-88385-511-9}}
* {{cite book
 | last1 = Shmerko | first1 = V. P.
 | last2 = Yanushkevich | first2 = Svetlana N. | author2-link = Svetlana Yanushkevich
 | last3 = Lyshevski | first3 = S. E.
 | year = 2009
 | title = Computer arithmetics for nanoelectronics
 | publisher = [[CRC Press]]
}}
* {{cite book
 | last = Smith | first = Frank
 | title = The Glass Wall: Why Mathematics Can Seem Difficult
 | url = https://archive.org/details/glasswallwhymath0000smit |url-access=registration |publisher=Teachers College Press
 | year = 2002
 | isbn = 978-0-8077-4242-6
}}
* {{cite book
 | last = Smith | first = Karl
 | title = The Nature of Modern Mathematics
 | edition = 3rd
 | publisher = Wadsworth
 | year = 1980
 | isbn = 978-0-8185-0352-8}}
* {{cite book
 | last1 = Sparks | first1 = F.
 | last2 = Rees | first2 = C.
 | title = A Survey of Basic Mathematics
 | publisher = McGraw-Hill
 | year = 1979
 | isbn = 978-0-07-059902-4
}}
* {{cite book
 | last = Taton | first= René
 | year = 1963
 | language = fr
 | title = Le Calcul Mécanique. Que Sais-Je ? n° 367
 | pages = 20–28
 | publisher = Presses universitaires de France
}}
* {{cite book
 | last = Stewart | first = James
 | title = Calculus: Early Transcendentals
 | edition = 4th
 | publisher = Brooks/Cole
 | year = 1999
 | isbn = 978-0-534-36298-0
 | url = https://archive.org/details/calculusearlytra00stew
}}
* {{cite book
 | last1 = Truitt | first1 = T.
 | last2 = Rogers | first2 = A.
 | title = Basics of Analog Computers
 | publisher = John F. Rider
 | year = 1960
 | id = {{LCC|QA76.4|T7}}
}}
* {{cite book
 | last = van de Walle |first=John |title=Elementary and Middle School Mathematics: Teaching developmentally |edition=5e |publisher=Pearson |year=2004 |isbn=978-0-205-38689-5 |url=https://archive.org/details/elementarymiddle00vand }}
* {{Cite book |last=Viro |first=Oleg |year=2001 |url=http://www.math.uu.se/~oleg/dequant/dequantH1.html |title=European Congress of Mathematics: Barcelona, July 10–14, 2000, Volume I. Dequantization of Real Algebraic Geometry on Logarithmic Paper |editor1-first=Carles |editor1-last=Cascuberta |editor2-first=Rosa Maria |editor2-last=Miró-Roig |editor3-first=Joan |editor3-last=Verdera |editor4-first=Sebastià |editor4-last=Xambó-Descamps |publisher=Birkhäuser |location=Basel |isbn=978-3-7643-6417-5 |series=Progress in Mathematics |volume=201 |pages=135–146 |arxiv=math/0005163 |zbl=1024.14026 |bibcode=2000math......5163V }}
* {{cite book
 | last = Williams | first = Michael
 |title=A History of Computing Technology |url=https://archive.org/details/historyofcomputi0000will |url-access=registration |publisher=Prentice-Hall |year=1985 |isbn=978-0-13-389917-7}}
* {{cite conference |last=Wynn |first=Karen |book-title=The Development of Mathematical Skills. |title=Numerical competence in infants |publisher=Taylor & Francis |year=1998 |isbn=0-86377-816-X}}
{{Refend}}