Lihat sumber bagi Penambahan

{{other uses}}
{{redirect|Tambah||Tambah (nyahkekaburan)}}
[[Fail:Addition01.svg|right|thumb|120px|3 + 2 = 5 dengan [[epal]], pilihan popular dalam buku teks<ref>Dari Enderton (p. 138): "...pilih dua set ''K'' dan ''L'' dengan kad ''K'' = 2 dan kad ''L'' = 3. Set jejari berguna; set epal lebih diminati oleh buku teks."</ref>]]
{{Operasi aritmetik}}
'''Penambahan''' (selalu ditandakan oleh [[simbol tambah]] "+") ialah satu daripada empat [[Operasi (matematik)|operations]] asas bagi [[aritmetik]]; Tiga operasi yang lain ialah [[penolakan]], [[pendaraban]] dan [[Pembahagian (matematik)|pembahagian]]. Penambahan dua [[Nombor asli|nombor bulat]] ialah jumlah amaun nilai itu digabungkan. Misalnya, dalam gambar sebelah, terdapat gabungan tiga biji epal dan dua biji epal bersama, menjadikan jumlahnya lima biji epal. Pemerhatian ini setara dengan [[Ungkapan (matematik)|ungkapan matematik]] {{nowrap|1="3 + 2 = 5"}} i.e., "3 ''tambah'' 2 adalah [[Kesamaan (matematik)|sama]] dengan 5".

Selain mengira barang, penambahan boleh juga ditakrifkan pada jenis nombor yang lain, seperti [[integer]], [[nombor nyata]] dan [[nombor kompleks]]. Hal ini sebahagian daripada [[aritmetik]], suatu cabang matematik. Dalam [[algebra]], bidang matematik yang lain, penambahan boleh dijalankan pada objek abstrak seperti [[vektor]] dan [[Matriks (matematik)|matriks]].

Penambahan ada beberapa sifat yang penting. Ia merupakan [[kalis tukar tertib]], bermakna urutan tidak penting, dan ia merupakan [[kalis kesekutuan|sekutuan]], bermakna apabila sesuatu tambah dengan lebih daripada dua nombor, susunan penambahan yang dijalankan tidak penting (lihat ''[[Penghasiltambahan]]''). Penambahan berulang {{num|1}} adalah sama dengan [[mengira]]; penambahan {{num|0}} tidak mengubah sebarang nombor. Penambahan mematuhi petua boleh ramal mengenai operasi yang berkaitan seperti [[penolakan]] dan [[pendaraban]].

Menjalankan penambahan merupakan satu daripada tugas berangka yang paling senang. Penambahan nombor yang amat kecil boleh didapat oleh kanak-kanak; tugas yang paling asas, {{nowrap|1 + 1}}, boleh dijalankan oleh bayi seusia lima bulan dan termasuk beberapa spesies haiwan yang lain. Dalam [[pendidikan rendah]], pelajar diajar menambah nombor dalam sistem [[perpuluhan]], bermula dengan digit tunggal dan mengatasi masalah yang lebih susah secara progresif. Bantuan mekanik dari [[sempoa]] kuno ke [[komputer]] moden, penyelidikan pelaksanaan penambahan yang paling cekap sambung ke hari ini.

==Tatatanda dan peristilahan==
[[Fail:PlusCM128.svg|right|120px|thumb|Simbol tambah]]
Penambahan ditulis menggunakan [[Tanda tambah dan tolak|tanda tambah]] "+" di antara sebutan; iaitu, dalam [[tatatanda sisipan]]. Hasilnya diungkap dengan [[tanda sama dengan]]. Misalnya,
:<math>1 + 1 = 2</math> ("satu tambah satu sama dengan dua")
:<math>2 + 2 = 4</math> ("dua tambah dua sama dengan empat")
:<math>1 + 2 = 3</math> ("satu tambah dua sama dengan tiga")
:<math>5 + 4 + 2 = 11</math> (lihat "kesekutuan" [[#Kesekutuan|di bawah]])
:<math>3 + 3 + 3 + 3 = 12</math> (lihat "pendaraban" [[#Operasi terhubung|di bawah]])

==Nota==
{{notelist}}

==Nota kaki==
{{reflist}}

==Rujukan==
{{refbegin}}
'''Sejarah'''
* {{cite book |first=José |last=Ferreirós |title=Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics |publisher=Birkhäuser |year=1999 |isbn=0817657495}}
* {{cite book |first=Louis |last=Karpinski |authorlink=Louis Charles Karpinski |title=The History of Arithmetic |publisher=Rand McNally |year=1925 |id={{LCC|QA21.K3}}}}
* {{cite book |first=Steven |last=Schwartzman |title=The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English |publisher=[[Mathematical Association of America|MAA]] |year=1994 |isbn=0883855119}}
* {{cite book |first=Michael |last=Williams |title=A History of Computing Technology |publisher=Prentice-Hall |year=1985 |isbn=0133899179}}

'''Matematik permulaan'''
* {{cite book |author1=Sparks, F. |author2=Rees C. |title=A Survey of Basic Mathematics |publisher=McGraw-Hill |year=1979 |isbn=0070599025}}

'''Pendidikan'''
* {{cite book |first=Edward |last=Begle |title=The Mathematics of the Elementary School |publisher=[[McGraw-Hill]] |year=1975 |isbn=0070043256}}
* [https://web.archive.org/web/20051228115904/http://www.cde.ca.gov/be/st/ss/mthmain.asp California State Board of Education mathematics content standards] Adopted December 1997, accessed December 2005.
* {{cite book |author1=Devine, D. |author2=Olson, J. |author3=Olson, M. |title=Elementary Mathematics for Teachers |edition=2e |publisher=[[John Wiley & Sons|Wiley]] |year=1991 |isbn=0471859478}}
* {{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=0309069955 |authorlink=United States National Research Council |url=http://www.nap.edu/books/0309069955/html/index.html |access-date=2019-01-07 |archive-date=2007-06-08 |archive-url=https://web.archive.org/web/20070608181717/http://www.nap.edu/books/0309069955/html/index.html |url-status=dead }}
* {{cite book |first=John |last=Van de Walle |title=Elementary and Middle School Mathematics: Teaching developmentally |edition=5e |publisher=Pearson |year=2004 |isbn=020538689X}}

'''Sains kognitif'''
* {{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=032500353X}}
* {{cite conference |first=Karen |last=Wynn |booktitle=The Development of Mathematical Skills. |title=Numerical competence in infants |publisher=Taylor & Francis |year=1998 |pages= |isbn=086377816X}}

'''Pendedahan matematik'''
* {{cite web |author=Bogomolny, 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 |accessdate=3 February 2006 |archiveurl=https://web.archive.org/web/20060426110928/http://www.cut-the-knot.org/do_you_know/addition.shtml |archivedate=April 26, 2006<!--DASHBot--> |deadurl=no }}
* {{cite book |first=William |last=Dunham |title=The Mathematical Universe |publisher=Wiley |year=1994 |isbn=0471536563}}
* {{cite book |first=Paul |last=Johnson |title=From Sticks and Stones: Personal Adventures in Mathematics |publisher=Science Research Associates |year=1975 |isbn=0574191151}}
* {{cite book |first=Carl |last=Linderholm |year=1971 |title=[[Mathematics Made Difficult]] |publisher=Wolfe |isbn=0723404151}}
* {{cite book |first=Frank |last=Smith |title=The Glass Wall: Why Mathematics Can Seem Difficult |publisher=Teachers College Press |year=2002 |isbn=0807742422}}
* {{cite book |first=Karl |last=Smith |title=The Nature of Modern Mathematics |edition=3rd |publisher=Wadsworth |year=1980 |isbn=0818503521}}

'''Matematik tinggi'''
* {{cite book |first=George |last=Bergman |title=An Invitation to General Algebra and Universal Constructions |edition=2.3 |publisher=General Printing |year=2005 |isbn=0965521141 |url=http://math.berkeley.edu/~gbergman/245/index.html }}
* {{cite book |first=Claude |last=Burrill |title=Foundations of Real Numbers |publisher=McGraw-Hill |year=1967 |id={{LCC|QA248.B95}}}}
* {{cite book |author1=Dummit, D. |author2=Foote, R. |title=Abstract Algebra |edition=2 |publisher=Wiley |year=1999 |isbn=0471368571}}
* {{cite book |first=Herbert |last=Enderton |title=Elements of Set Theory |publisher=[[Academic Press]] |year=1977 |isbn=0122384407}}
* {{cite book |first=John |last=Lee |title=Introduction to Smooth Manifolds |publisher=Springer |year=2003 |isbn=0387954481}}
* {{cite book |first=John |last=Martin |title=Introduction to Languages and the Theory of Computation |publisher=McGraw-Hill |edition=3 |year=2003 |isbn=0072322004}}
* {{cite book |first=Walter |last=Rudin |title=Principles of Mathematical Analysis |edition=3 |publisher=McGraw-Hill |year=1976 |isbn=007054235X}}
* {{cite book |first=James |last=Stewart |title=Calculus: Early Transcendentals |edition=4 |publisher=Brooks/Cole |year=1999 |isbn=0534362982}}

'''Penyelidikan matematik'''
* {{cite journal |author1=Akian, Marianne |author2=Bapat, Ravindra |author3=Gaubert, Stephane |title=Min-plus methods in eigenvalue perturbation theory and generalised Lidskii-Vishik-Ljusternik theorem |journal=INRIA reports |year=2005 |arxiv=math.SP/0402090}}
* {{cite conference |author=[[John C. Baez|Baez, J.]] |author2=Dolan, J. |booktitle=Mathematics Unlimited— 2001 and Beyond. From Finite Sets to Feynman Diagrams |year=2001 |pages=29 |arxiv=math.QA/0004133 |isbn=3540669132}}
* Litvinov, Grigory; Maslov, Victor; Sobolevskii, Andreii (1999). [https://arxiv.org/abs/math.SC/9911126 Idempotent mathematics and interval analysis]. ''[http://www.springerlink.com/openurl.asp?genre=article&eissn=1573-1340&volume=7&issue=5&spage=353 Reliable Computing] {{Webarchive|url=https://archive.today/20130203014259/http://www.springerlink.com/openurl.asp?genre=article&eissn=1573-1340&volume=7&issue=5&spage=353 |date=2013-02-03 }}'', Kluwer.
* {{cite journal |first=Jean-Louis |last=Loday |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=Mikhalkin |first=Grigory |year=2006 |arxiv=math.AG/0601041 |zbl=1103.14034 |editor1-last=Sanz-Solé |editor1-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=978-3037190227 |pages=827–852}}
* {{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=3764364173 |series=Progress in Mathematics |volume=201 |pages=135–146 |arxiv=math/0005163 |zbl=1024.14026 |postscript=. |bibcode=2000math......5163V }}

'''Pengkomputeran'''
* {{cite book |author1=Flynn, M. |author2=Oberman, S. |title=Advanced Computer Arithmetic Design |publisher=Wiley |year=2001 |isbn=0471412090}}
* {{cite book |author1=Horowitz, P. |author2=Hill, W. |title=The Art of Electronics |edition=2 |publisher=Cambridge UP |year=2001 |isbn=0521370957}}
* {{cite book |first=Albert |last=Jackson |title=Analog Computation |publisher=McGraw-Hill |year=1960 |id={{LCC|QA76.4|J3}}}}
* {{cite book |author1=Truitt, T. |author2=Rogers, A. |title=Basics of Analog Computers |publisher=John F. Rider |year=1960 |id={{LCC|QA76.4|T7}}}}
* {{cite book |ref=MARG |language=fr |title=Histoire des Instruments et Machines à Calculer, Trois Siècles de Mécanique Pensante 1642–1942 |first=Jean |last=Marguin |year=1994 |publisher=Hermann |location= |isbn=978-2705661663}}
* {{cite book |ref=TATON63 |language=fr |title=Le Calcul Mécanique. Que Sais-Je ? n° 367 |first=René |last=Taton |year=1963 |pages=20–28 |publisher=Presses universitaires de France |location= |isbn=}}
{{refend}}

==Bacaan lanjut==
* {{cite conference |last1=Baroody |first1=Arthur |last2=Tiilikainen |first2=Sirpa |booktitle=The Development of Arithmetic Concepts and Skills. Two perspectives on addition development |year=2003 |page=75 |isbn=080583155X |publisher=Routledge}}
* {{cite book |last1=Davison |first1=David M. |last2=Landau |first2=Marsha S. |last3=McCracken |first3=Leah |last4=Thompson |first4=Linda |title=Mathematics: Explorations & Applications |edition=TE |publisher=Prentice Hall |year=1999 |isbn=0134358171}}
* {{cite book |first1=Lucas N.H. |last1=Bunt |first2=Phillip S. |last2=Jones |first3=Jack D. |last3=Bedient |title=The Historical roots of Elementary Mathematics |publisher=Prentice-Hall |year=1976 |isbn=0133890155}}
* {{cite journal |last=Poonen |first=Bjorn |year=2010 |title=Addition |url=http://www.girlsangle.org/page/bulletin.php |journal=Girls' Angle Bulletin  |volume=3 |issue=3-5 |publisher=Girls' Angle |issn=2151-5743}}
* {{cite conference |first=J. Fred |last=Weaver |booktitle=Addition and Subtraction: A Cognitive Perspective. Interpretations of Number Operations and Symbolic Representations of Addition and Subtraction |year=1982 |page=60 |isbn=0898591716 |publisher=Taylor & Francis}}

{{Aritmetik permulaan}}
{{Hiperoperasi}}

[[Kategori:Aritmetik permulaan]]
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