สมบ, การเปล, ยนหม, ในคณ, ตศาสตร, งกฤษ, associativity, เป, นสมบ, หน, งท, สามารถม, ได, ของการดำเน, นการทว, ภาค, งน, พจน, วดำเน, นการเด, ยวก, นต, งแต, สองต, วข, นไป, การดำเน, นการสามารถกระทำได, โดยไม, สำค, ญว, าลำด, บของต, วถ, กดำเน, นการจะเป, นอย, างไร, นหมายควา. inkhnitsastr smbtikarepliynhmu xngkvs associativity epnsmbtihnungthisamarthmiidkhxngkardaeninkarthwiphakh sungniphcnthimitwdaeninkarediywkntngaetsxngtwkhunip kardaeninkarsamarthkrathaidodyimsakhywaladbkhxngtwthukdaeninkarcaepnxyangir nnhmaykhwamwa kariswngelbephuxbngkhbladbkarkhanwninniphcn caimsngphltxphllphthsudthay twxyangechn 5 2 1 5 2 1 8 dd niphcnkhangsaycabwk 5 kb 2 kxnaelwkhxybwk 1 swnniphcnkhangkhwacabwk 2 kb 1 kxnaelwkhxybwk 5 imwaladbkhxngwngelbcaepnxyangir phlbwkkhxngniphcnkethakb 8 imepliynaeplng aelaenuxngcaksmbtiniepncringinkarbwkkhxngcanwncringid eraklawwa karbwkkhxngcanwncringepnkardaeninkarthi epliynhmuid associative kh imkhwrsbsnrahwangsmbtikarepliynhmukbsmbtikarslbthi smbtikarslbthiepnkarepliynladbkhxngtwthukdaeninkarinniphcn inkhnathismbtikarepliynhmuimidslbtwthukdaeninkarehlann ephiyngaekhepliynladbkarkhanwn echntwxyangtxipni 5 2 1 2 5 1 dd imichtwxyangkhxngsmbtikarepliynhmu ephraawa 2 kb 5 slbthiknkardaeninkarepliynhmuidmimakmayinkhnitsastr aeladwykhxethccringthiwaokhrngsrangechingphichkhnitswnihycaepntxngmikardaeninkarthwiphakhthiepliynhmuidepnswnprakxb xyangirktamkardaeninkarhlayxyangthisakhyk epliynhmuimid hrux imepliynhmu non associative echnphlkhunikhwkhxngewketxrwikhetxr orenleemssi enuxha 1 niyam 2 twxyang 3 kardaeninkarimepliynhmu 4 duephimniyam aekikhkahndkardaeninkarthwiphakh bnest S eracaklawwakardaeninkarnn epliynhmuid thahak x y z S x y z x y z displaystyle forall x y z in S x y z x y z dd aelaenuxngcakladbkhxngkardaeninkarimmikhwamsakhy eracungxacimcaepntxngiswngelb dngni x y z displaystyle x y z dd xyangirktam singsakhythicatxngcdcakhux karepliynladbkhxngkardaeninkarcatxngimthaihtwthukdaeninkarepliyntaaehnngipphayinniphcnkahndfngkchnthwiphakh f A A B eracaklawwafngkchnnn epliynhmuid thahak x y z A f f x y z f x f y z displaystyle forall x y z in A f f x y z f x f y z dd twxyang aekikhtwxyangbangswnkhxngkardaeninkarepliynhmumidngni inelkhkhnit karbwkaelakarkhunsamarthepliynhmuid x y z x y z x y z x y z x y z x y z x y z R displaystyle left begin matrix x y z x y z x y z quad x y z x y z x y z qquad qquad qquad quad end matrix right forall x y z in mathbb R dd karbwkaelakarkhunkhxngcanwnechingsxnaelakhwxethxreniynksamarthepliynhmuid sahrbkarbwkkhxngxxkotheniynnnepliynhmuid aetkarkhunkhxngxxkotheniynimepliynhmu fngkchntwharrwmmakaelatwkhunrwmnxykepliynhmuidgcd gcd x y z gcd x gcd y z gcd x y z lcm lcm x y z lcm x lcm y z lcm x y z x y z Z displaystyle left begin matrix operatorname gcd operatorname gcd x y z operatorname gcd x operatorname gcd y z operatorname gcd x y z quad operatorname lcm operatorname lcm x y z operatorname lcm x operatorname lcm y z operatorname lcm x y z quad end matrix right forall x y z in mathbb Z dd enuxngcakkaraeplngechingesnkhuxfngkchnthisamarthnaesnxiddwykarkhunemthriks sungepnkarnaesnxkhxngkarprakxbfngkchn dngnneracungsamarthsrupidthnthiwakarkhunemthrikssamarthepliynhmuid xinetxreskchnaelayueniynkhxngest samarthepliynhmuiddngni A B C A B C A B C A B C A B C A B C for all sets A B C displaystyle left begin matrix A cap B cap C A cap B cap C A cap B cap C quad A cup B cup C A cup B cup C A cup B cup C quad end matrix right mbox for all sets A B C dd tha M epnestesthnung aela S aethnestkhxngfngkchnthnghmdcak M ipyng M aelwkardaeninkarkhxngfngkchnprakxbbn S epliynhmuid f g h f g h f g h f g h S displaystyle f circ g circ h f circ g circ h f circ g circ h qquad forall f g h in S dd inkrnithwip kahndihest M N P Q aelakarcbkhu h M N g N P f P Q aelw f g h f g h f g h displaystyle f circ g circ h f circ g circ h f circ g circ h dd dngnn karcbkhucungepnkardaeninkarepliynhmuidesmxkardaeninkarimepliynhmu aekikhkahndkardaeninkarthwiphakh bnest S eracaklawwakardaeninkarnn epliynhmuimid thahak x y z S x y z x y z displaystyle exists x y z in S x y z neq x y z dd kardaeninkarechnnn ladbkhxngkarkhanwncungmikhwamsakhy echnkarlb karhar aelakarykkalng 5 3 2 5 3 2 displaystyle 5 3 2 neq 5 3 2 4 2 2 4 2 2 displaystyle 4 div 2 div 2 neq 4 div 2 div 2 2 1 2 2 1 2 displaystyle 2 1 2 neq 2 1 2 dd ekhruxnghmaywngelbcungthukichephuxaesdngladbkhxngkardaeninkar emuxmikardaeninkarehlanimakkwahnungkhrnginniphcn xyangirktam nkkhnitsastridyxmrbladbkhwamsakhykhxngkardaeninkarthiimepliynhmuhlaychnid epnhlkkarinkarekhiynephuxhlikeliyngkarichwngelb aebngxxkidepnsxngpraephth idaekkardaeninkarthicdklumthangsay x y z x y z w x y z w x y z etc w x y z S displaystyle left begin matrix x y z x y z qquad qquad quad w x y z w x y z quad mbox etc qquad qquad qquad qquad qquad qquad end matrix right forall w x y z in S dd aelakardaeninkarthicdklumthangkhwa x y z x y z w x y z w x y z etc w x y z S displaystyle left begin matrix x y z x y z qquad qquad quad w x y z w x y z quad mbox etc qquad qquad qquad qquad qquad qquad end matrix right forall w x y z in S dd duephim aekikhsmbtikarslbthi smbtikaraeckaecngekhathungcak https th wikipedia org w index php title smbtikarepliynhmu amp oldid 8971012, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,