
selam-spensor sett

ganit mein, aur vishesh roop seey ankganitiya sanyojan mein, ack selam-spensor sett sankhyaon kaa ack sett haye jisamen seey koee teen ankganitiya pragati kaa nirmaan karate hain. selam-spensor sett koo 3-app-free anukram yaa pragati-mukt sett bhee kahaa jaataa haye. unhein gair-ausat samooh bhee kahaa gayaa haye, lekin iss shabd kaa upayog purnankon key ack samooh koo niroopit karane key liye bhee kiya gayaa haye, jinamen seey kissy koo bhee anya sankhyaon key kissy bhee upasamuchchay key ausat key roop mein praapt naheen kiya jaa sakata haye. salem-spensor sett kaa naam rafale salem aur donald see key naam parr rakhaa gayaa haye. spensor, jinhone 1942 mein dikhaaya kii selam-spensor sett kaa aakar lagbhag raikhik hoe sakata haye. haalaanki, closs roth kii ack baad kii pramey seey pataa chalata haye kii aakar hamesha raikhik seey cumm hotaa haye.
udaaharan.
sootra _ 1 key liye sootra _ 2 key sabse chhote maan aise hain kii sootra _ 3 seey sootra _ 2 taka kii sankhyaon kaa ack sootra _ 5-tatva selam-spensor sett haye
udaaharan key liye, 1 seey 14 taka kii sankhyaon mein seey aathh sankhyaaen hain.
advitiya sabse badaa selam-spensor sett banaate hain.
iss udaaharan koo ack anant selam-spensor sett, stanley anukram key tatvon mein ack jodkar sthanantarit kiya jaataa haye.
una sankhyaon kaa joe, jaba ack trikoniya sankhya key roop mein likhi jaati haye, kewal ankon 0 aur 1 kaa upayog karati haye. yeh anukram shabdakosh kii drishti seey pahala anant selam-spensor sett haye. cubes dwara ack aur anant selem-spensor sett diyaa jaataa haye.
yeh leonhard euler kii ack pramey haye kii koee bhee teen cubes ankganitiya pragati mein naheen hain.
aakar.
1942 mein, selam aur spensor ney ack pramaan prakaashit kiya kii sootra _ 3 seey sootra _ 2 taka kii seema mein purnankon mein badey selam-spensor sett hain, aakar sootra _ 8 key. iss abhivyakti kaa bhaajak badey oh sanketan kaa upayog kartaa haye, aur sootra _ 2 kii kissy bhee shakti kii tulanaa mein adhik dheere-dheere badhata haye, isaliye selam aur spensor dwara paae jaane vaale seton kaa aakar lagbhag raikhik hotaa haye. iss baadhya ney paul erdos aur paal turran key ack anuman koo galat saabit kiya kii iss tarah key sett kaa aakar kissy sootra _ 11 key liye adhikatam sootra _ 10 hoe sakata haye.
1946 mein felix behrend ney salem aur spensor key nirmaan mein sudhaar kiya, jinhone aakar sootra _ 12 key sett paae.
1952 mein, closs roth ney roth kii pramey koo saabit kiya kii ack selam-spensor sett kaa aakar sootra _ 13 honah chaahiye. isaliye, halanki selam, spensor aur herend dwara nirmit seton key aakar lagbhag raikhik hain, unhein sudharna aur aise seton koo dhoondhana sambhav naheen haye jinka aakar vaastav mein raikhik haye. yeh parinam purnankon key seton key ghanatva parr zemerady key pramey kaa ack vishesh mamla bunn gayaa joe lambe ankganitiya pragati seey bachate hain. selam-spensor sett parr roth kii seema koo beejganitiya sankhyaon key diophantine sanniktan parr roth kii pramey seey alag karane key liye, iss parinam koo "ankganitiya pragati parr roth kii pramey" kahaa gayaa haye. roth kii pramey mein kaee atirikt sudhaaron key baad, ack selam-spensor sett kaa aakar sootra _ 14 saabit huaa haye. sootra _ 15 kii ack behtar seema (kuchh sootra _ 11 key liye jisaki spasht roop seey ganana naheen kii gaee haye) 2020 mein ghoshit kii gaee thee, lekin abhee taka referee aur prakaashit naheen kiya gayaa haye. 2023 mein sootra _ 17 kii ack naee seema paaee gaee aur chaar dinn baad parinam koo sootra _ 18 mein thodaa sudhaar key saath saral banaaya gayaa, inn parinamon koo abhee taka sandarbhit aur prakaashit bhee naheen kiya gayaa haye.
nirmaan.
ack selem-spensor sett (joe kii behrend kii seema seey kaafee chhota aakar kaa hotaa haye) key liye ack saral nirmaan tri-sankhya sankhya kaa chayan karna haye joe kewal ankon 0 aur 1 kaa upayog kartaa haye, naa kii 2. aisaa sett pragati-mukt honah chaahiye, kyonki yadi isake dou tatva sootra _ 19 aur sootra _ 20 ack ankganitiya pragati key pahale aur dusare sadasya hain, tou teesare sadasya key paas cumm seey cumm mahatvapurna ank kii sthiti mein ank dou honah chaahiye jahaan sootra _ 19 aur sootra _ 20 bhinn houn. chitran iss roop kaa ack samooh dikhaata haye, teen ankon kii trikoniya sankhyaon key liye (0 key bajaay sabse chhote tatva 1 banaane key liye ack dwara sthanantarit).
bearand kaa nirmaan ack samaan vichaar kaa upayog kartaa haye, ack badey visham mool sootra key liye _ 23. usake sett mein way sankhyaaen hoti hain jinake ank sootra _ 24 seey sootra _ 25 taka kii seema taka seemit hotey hain (taaki inn sankhyaon key jodd mein koee wahan naheen hotaa haye), atirikt baadha key saath kii ankon key vargon kaa yog kuchh chunaa huaa moolya sootra _ 5 haye. yadi pratyek sankhya key ankon koo ack vector key nirdeshank key roop mein maanaa jaataa haye, tou yeh baadha parinami vector sthaan mein ack gole kaa varnan karati haye, aur uttalata dwara iss gole parr dou alag-alag moolyon kaa ausat usa gole key aantarik hoga naa kii usa parr. isaliye, yadi vartak key samooh key dou tatva ack ankganitiya pragati key antim bindu hain, tou pragati kaa madhya moolya (unakaa ausat) sett mein naheen hoga. iss prakaar, parinami samooh pragati-mukt haye.
sootra _ 27 key saavdhaanipoorvak chayan key saath, aur ankon key vargon key sabse adhik baar honey vaale yog key roop mein sootra _ 5 key chayan key saath, dekhein apani seema praapt kartaa haye.
1953 mein, leo moser ney saabit kiya kii ack hii anant selem-spensor anukram haye joe harr upsarg parr samaan asymptotic ghanatva praapt kartaa haye jaisa kii behrend kaa nirmaan haye.
ack gole key ander binduon key uttal patwar parr vichaar karke, ack gole parr binduon key sett key bajaay,
sootra _ 29 key ack kaarak dwara nirmaan mein sudhaar karna sambhav haye. haalaanki, yeh oopar bataae gaye roop mein aakar koo prabhaavit naheen kartaa haye.
saamaanyikaran.
selam-spensor sett (3-app-free sett) kii dhaarana koo sootra-5-app-free sett key liye saamaanyikrit kiya jaa sakata haye, jisamen sootra-5 tatva ack ankganitiya pragati banaate hain yadi aur kewal tabhi jaba way sabhi samaan houn. badey sootra _ 5-aeye. pee.-mukt seton kaa nirmaan diyaa.
computational parinam.
gassarc, glain aur cruscal ney sootra _ 33 key badey upasamuchchay key liye vibhinn computational vidhiyon kii tulanaa kii haye jisamen koee ankganitiya pragati naheen haye. inn vidhiyon kaa upayog karke unhone sootra _ 34 key liye iss tarah key sabse badey sett kaa sateek aakar paaya. unake parinamon mein sootra _ 2 key vibhinn moolyon key liye kaee naee seemaaen shamil hain, joe shakha-aur-baadhya algorithm dwara paaee jaati hain joe raikhik prograaming aur samasya-vishisht shodh kaa upayog karate hain taaki usa aakar koo bandha jaa sakey jise khoj vriksh kii kissy bhee shakha mein praapt kiya jaa sakata haye. ack shodhaatmak joe unhein vishesh roop seey prabhaavi paaya gayaa vaha thaa "thurd methed", jisamen formula _ 2 key liye ack selem-spensor sett kii dou sthanantarit pratiyon koo formula _ 37 key liye ack sett key pahale aur antim teesare hisse mein rakhaa jaataa haye.
anuprayog.
ruzaa-szemerady samasya key sambandh mein, salem-spensor sett kaa upayog ghaney graph key nirmaan key liye kiya gayaa haye jisamen pratyek kinara ack advitiya trikon seey sambandhit haye. 
saiddhaantik computer vigyaan mein bhee selam-spensor sett kaa upayog kiya gayaa haye. way tez matricks gunan key liye coppersmith-vinograd algorithm key design mein aur kushal gair-paraspar shoonya-gyaan pramaan key nirmaan mein upayog kiye gaye hain. haal hii mein, unakaa upayog graph spanners key liye aakar kii nichali seema dikhaane key liye kiya gayaa haye, aur subset summ samasya kii majboot ghaatiya samay parikalpana adharit kathorta.
inn seton koo manoranjak ganit mein ack ganitiya shatranj samasya key liye bhee lagu kiya jaa sakata haye.
ack sootra _ 38 shatranj board key mukhya vikarn parr jitani sambhav hoe utani cumm raniyon koo rakhna taaki board key sabhi vargon parr hamla kiya jaa sakey. vikarn vargon kaa samooh joe khaali rahata haye, usey ack selam-spensor sett banaana chaahiye, jisamen sabhi moolyon kii samaan samaantaa (sabhi visham yaa sabhi summ) hoti haye.
raniyon kaa sabse chhota sambhav samooh sootra _ 33 mein visham sankhyaon key sabse badey selam-spensor subset kaa poorak haye.
iss selem-spensor upasamuchchay koo sootra _ 40 mein sabhi sankhyaon key selem-spensor upasamuchchay mein moolyon seey ack koo doguna aur ghataakar paaya jaa sakata haye.

