thulyavum vichitravumaaya oordinalukal

ganithashaasthrathil, eratta, otta oordinalukal swaabhaavika samkhyakalil ninnu oordinal samkhyakal vare paarity enna ashayam vyaapippikkunnu. chila traansphinait induction proofil avaa upayogapradamaanu.
saahithyathil oru oordinal α-yude thulyathayude chila thulyamaaya nirvachanangal adangiyirikkunnu
eratta poornnasamkhyakalude kaaryatthil ninnu vyathyasthamayi, oraalkk oordinal samkhyakale oordinal gunana roopathinte oordinal nambarukalaayi visheshippikkaan kazhiyilla, athinaal pothuve, eratta oordinal β + β ennum oordinal nambar ennum prakadippikkaan kazhiyilla.
thulyamalla.
oordinal paarittiyude lalithamaaya prayogam cardinal aditionulla idempottense niyamamaan (well-oordaring sidhaantham nalkiyirikkunnu). ananthamaaya kardinal κ, allengil saadhaaranayaayi eathenkilum paridhi oordinal κ nalkiyaal, κ athinte eratta oordinalukalude upavibhagathinum otta oordinalukalude upavibhagathinum oordar-isomorphic aanu. athinaal oraalkk cardinal thukayund. 

