
conway sanketan (gaanth siddhant)

gaanth siddhant mein, johnn horton conway dwara aavishkaar kiya gayaa conway sanketan, gaanthon kaa varnan karane kaa ack tarika haye joe unake kaee gunon koo spasht kartaa haye. yeh ise banaane key liye uljhanon parr kuchh sanchaalan kaa upayog karke ack gaanth banaata haye.
buniyaadi avadhaaranaaen.
ulajhanen.
samkon sanketan mein, ulajhan aam taur parr beejganitiya 2-ulajhan hotey hain. iska matlab haye kii unake ulajhan aarekh mein aarekh key kinare parr 2 chaap aur 4 bindu hotey hain; isake alawa, way kanave sanchaalan kaa upayog karke tarksangat ulajhan seey baney hotey hain.
[aisaa prateet hotaa haye kii nimnalikhit kewal purnank yaa 1/n parimeya uljhanon kaa varnan karane kaa prayaas curr rahey hain.]
kewal sakaratmak crossing seey yukt uljhanon koo crossing kii sankhya seey darshaaya jaataa haye, yaa yadi kewal nakaratmak crossing hain tou ise ack nakaratmak sankhya seey darshaaya jaataa haye. yadi chapon koo paar naheen kiya jaataa haye, yaa redemister chaalon key saath ack uncross sthiti mein parivartit kiya jaa sakata haye, tou ise 0 yaa φ ulajhan kahaa jaataa haye, joe ulajhan key abhivinyas parr nirbhar kartaa haye.
uljhanon parr sanchaalan.
yadi ack ulajhan, "a", nw-se rekha parr paraavartit hoti haye, tou ise "−a" dwara darshaaya jaataa haye. (dhyaan dein kii yeh crossing kii nakaratmak sankhya key saath ack ulajhan seey alag haye.) uljhanon key teen dwiaadhaari sanchaalan hotey hain, "yog", "utpaad" aur "parivibhajan", haalaanki sabhi koo ulajhan jodd aur nishedh kaa upayog karke samajhaaya jaa sakata haye. ulajhan utpaad, "a b", "−a + b" key barabar haye. aur parimaap yaa "a, b", "−a + −b" key barabar haye.
unnat avadhaaranaaen.
tarksangat ulajhan tabhi samatulya hoti hain jaba unake ansh samaan houn. iss tathya kaa ack sulabh pramaan (coffman aur lambropolou 2004) mein diyaa gayaa haye. ack tarankan chihn seey pahale kii sankhya, "*", bahu-hadron sankhya koo darshaati haye; kaee tarankan sanket dete hain kii usa sankhya key kaee bahu-header maujood hain.

