D'Angelo, John P.; West, Douglas B. (2000), Mathematical Thinking / Problem-Solving and Proofs (2nd ed.), Prentice-Hall, ISBN978-0-13-014412-6
Keith Devlin, The Joy of Sets. Springer Verlag, 2nd ed., 1993, ISBN 0-387-94094-4, pp. 7–8
Abraham Adolf Fraenkel, Yehoshua Bar-Hillel, Azriel Lévy, Foundations of set theory, Elsevier Studies in Logic Vol. 67, Edition 2, revised, 1973, ISBN 0-7204-2270-1, p. 33
Gaisi Takeuti, W. M. Zaring, Introduction to Axiomatic Set Theory, Springer GTM 1, 1971, ISBN 978-0-387-90024-7, p. 14
George J. Tourlakis, Lecture Notes in Logic and Set Theory. Volume 2: Set theory, Cambridge University Press, 2003, ISBN 978-0-521-75374-6, pp. 182–193
สิงหาคม 16, 2021
หลายส, งอ, นด, หร, เพ, งกฤษ, tuple, เป, นว, ตถ, ทางคณ, ตศาสตร, ชน, ดหน, โดย, displaystyle, งอ, นด, เป, นลำด, บของส, displaystyle, เม, displaystyle, เป, นจำนวนเต, มไม, เป, นลบ, โดยท, นด, บของส, งต, าง, ในน, นม, ความสำค, ญและไม, สามารถสล, บท, ได, ณสมบ, งกล, าวน,. hlaysingxndb hrux thuephil xngkvs tuple epnwtthuthangkhnitsastrchnidhnung ody n displaystyle n singxndb epnladbkhxngsing n displaystyle n sing emux n displaystyle n epncanwnetmimepnlb odythixndbkhxngsingtang inhlaysingxndbnnmikhwamsakhyaelaimsamarthslbthiid khunsmbtidngklawniexngthaihhlaysingxndbaetktangcakest karekhiynhlaysingxndbmkekhiynrabusingtang inhlaysingxndbnn khndwyekhruxnghmayculphakh aelakhrxbdwyekhruxnghmaywngelb echn 2 7 4 1 7 displaystyle 2 7 4 1 7 epnhasingladb sungaetktangcakhasingxndb 7 7 1 2 4 displaystyle 7 7 1 2 4 hakhlaysingxndbnnmisxngsing camichuxeriykechphaawakhuxndbinkhnitsastr hlaysingxndbsamarthnaipichxthibaywtthuthangkhnitsastrchnidxun id echnewketxr swninkarekhiynopraekrmkhxmphiwetxr odyechphaakarekhiynopraekrmechingfngkchn hlaysingxndbepnchnidkhxngtwaeprthimikhwamsakhy nxkcakniaelwyngphbkarichhlaysingxndbinsastrxun echn phasasastr 1 aelaprchya 2 enuxha 1 khunsmbti 2 niyam 2 1 niyamdwyfngkchn 2 2 niyamdwykhuladbsxn 2 3 niyamdwyestsxn 3 xangxingkhunsmbti aekikhodythwipaelw cakahndih n displaystyle n singxndbethakn ktxemuxsingthixyuintaaehnngtrngknnnethaknthnghmd nnkhux a 1 a 2 a n b 1 b 2 b n displaystyle a 1 a 2 ldots a n b 1 b 2 ldots b n ktxemux a 1 b 1 a 2 b 2 a n b n displaystyle a 1 b 1 text a 2 b 2 text ldots text a n b n khunsmbtidngklawthaihhlaysingxndbmikhwamaetktangcakest dwyehtuphldngtxipni hlaysingxndbxacmiaetlasingepncanwnmakkwahnungkid aelacanwnkhxngsingthiaetktangknthaihhlaysingxndbepliynip echn hlaysingxndb 1 2 2 3 1 2 3 displaystyle 1 2 2 3 neq 1 2 3 aetest 1 2 2 3 1 2 3 displaystyle 1 2 2 3 1 2 3 xndbkhxngsingtang inhlaysingxndbnnmikhwamsakhyaelaimsamarthslbthiid echn hlaysingxndb 1 2 3 3 2 1 displaystyle 1 2 3 neq 3 2 1 aetest 1 2 3 3 2 1 displaystyle 1 2 3 3 2 1 hlaysingxndbcamicanwnsingimepnxnnt swnestnncamicanwnsmachikepnxnnthruximkidniyam aekikhhlaysingxndbnnsamarthkahndniyamidhlayaebbodythiyngsxdkhlxngkbkhunsmbtithitxngkarkhangtn dngtxipni niyamdwyfngkchn aekikh inechingthvsdiest xacniyam n displaystyle n singxndbepnfngkchn F thimiodemnepnest X khxngtaaehnngtang inhlaysingxndb aelaokhodemnepnest Y khxngsingtang inhlaysingxndb nnkhux niyamih n displaystyle n singxndb khux a 1 a 2 a n X Y F displaystyle a 1 a 2 dots a n equiv X Y F emux X 1 2 n Y a 1 a 2 a n F 1 a 1 2 a 2 n a n displaystyle begin aligned X amp 1 2 dots n Y amp a 1 a 2 ldots a n F amp 1 a 1 2 a 2 ldots n a n end aligned hruxxacekhiyninruplalxngidepn a 1 a 2 a n F 1 F 2 F n displaystyle a 1 a 2 dots a n F 1 F 2 dots F n niyamdwykhuladbsxn aekikh inechingthvsdiestsamarthniyam n displaystyle n singxndbidxikwithihnung nnkhux karichkhuxndbsxn withikarnismmtiwamikarkahndniyamkhuxndbiweriybrxyaelw caknnnamakhyayepnniyamkhxng n displaystyle n singxndb odyniyamaebbewiynekiddngni 0 singxndbsamarthaethniddwyestwang displaystyle emptyset n displaystyle n singxndb emux n gt 0 displaystyle n gt 0 niyamihepnkhuxndbthimismachiktwhnaepnsingsingaerk aelasmachiktwhlngepn n 1 displaystyle n 1 singxndbkhxngsingthiehlux nnkhux a 1 a 2 a 3 a n a 1 a 2 a 3 a n displaystyle a 1 a 2 a 3 ldots a n a 1 a 2 a 3 ldots a n emuxichniyamniaebbewiynekidcaidwa a 1 a 2 a 3 a n a 1 a 2 a 3 a n displaystyle a 1 a 2 a 3 ldots a n a 1 a 2 a 3 ldots a n emptyset ldots twxyangechn 1 2 3 1 2 3 1 2 3 4 1 2 3 4 displaystyle begin aligned 1 2 3 amp 1 2 3 emptyset 1 2 3 4 amp 1 2 3 4 emptyset end aligned hruxxackahndniyaminthisthangtrngkhamkid dngni 0 singxndbsamarthaethniddwyestwang displaystyle emptyset n displaystyle n singxndb emux n gt 0 displaystyle n gt 0 niyamihepnkhuxndbthimismachiktwhlngepnsingsingsudthay aelasmachiktwhnaepn n 1 displaystyle n 1 singxndbkhxngsingthiehlux nnkhux a 1 a 2 a 3 a n a 1 a 2 a 3 a n 1 a n displaystyle a 1 a 2 a 3 ldots a n a 1 a 2 a 3 ldots a n 1 a n emuxichniyamaebbewiynekidcaidwa a 1 a 2 a 3 a n a 1 a 2 a 3 a n displaystyle a 1 a 2 a 3 ldots a n ldots emptyset a 1 a 2 a 3 ldots a n twxyangechn 1 2 3 1 2 3 1 2 3 4 1 2 3 4 displaystyle begin aligned 1 2 3 amp emptyset 1 2 3 1 2 3 4 amp emptyset 1 2 3 4 end aligned niyamdwyestsxn aekikh emuxnaniyamkhangtnmaprakxbkb niyamkhuxndbkhxngkhurathawski caidniyamkhxng n displaystyle n singxndb thiepnniyaminrupthvsdiestaeth dngni 0 singxndbsamarthaethniddwyestwang displaystyle emptyset kahndih x displaystyle x epn n displaystyle n singxndb a 1 a 2 a n displaystyle a 1 a 2 ldots a n aelakahndih x b a 1 a 2 a n b displaystyle x rightarrow b equiv a 1 a 2 ldots a n b caidwa x b x x b displaystyle x rightarrow b equiv x x b eriykwa x displaystyle x echuxmkb b displaystyle b twxyangechn 1 1 1 1 1 2 1 2 1 1 2 1 1 2 1 2 3 1 2 3 1 2 1 2 3 1 1 2 1 1 2 3 displaystyle begin array lclcl amp amp amp amp emptyset amp amp amp amp 1 amp amp rightarrow 1 amp amp 1 amp amp amp amp emptyset emptyset 1 amp amp amp amp 1 2 amp amp 1 rightarrow 2 amp amp 1 1 2 amp amp amp amp emptyset emptyset 1 amp amp amp amp emptyset emptyset 1 2 amp amp amp amp 1 2 3 amp amp 1 2 rightarrow 3 amp amp 1 2 1 2 3 amp amp amp amp emptyset emptyset 1 amp amp amp amp emptyset emptyset 1 2 amp amp amp amp emptyset emptyset 1 amp amp amp amp emptyset emptyset 1 2 3 end array xangxing aekikh http www oxfordreference com view 10 1093 acref 9780199202720 001 0001 acref 9780199202720 e 2276 http www oxfordreference com view 10 1093 acref 9780199541430 001 0001 acref 9780199541430 e 2262 D Angelo John P West Douglas B 2000 Mathematical Thinking Problem Solving and Proofs 2nd ed Prentice Hall ISBN 978 0 13 014412 6 Keith Devlin The Joy of Sets Springer Verlag 2nd ed 1993 ISBN 0 387 94094 4 pp 7 8 Abraham Adolf Fraenkel Yehoshua Bar Hillel Azriel Levy Foundations of set theory Elsevier Studies in Logic Vol 67 Edition 2 revised 1973 ISBN 0 7204 2270 1 p 33 Gaisi Takeuti W M Zaring Introduction to Axiomatic Set Theory Springer GTM 1 1971 ISBN 978 0 387 90024 7 p 14 George J Tourlakis Lecture Notes in Logic and Set Theory Volume 2 Set theory Cambridge University Press 2003 ISBN 978 0 521 75374 6 pp 182 193ekhathungcak https th wikipedia org w index php title hlaysingxndb amp oldid 5883478, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
