@MISC{ORDINAL1.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {The Ordinal Numbers},
  SUBTITLE = {Transfinite Induction and Defining by Transfinite Induction},
  DAY = {20},
  MONTH = {March},
  YEAR = {1989},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {In the beginning of the article we show some consequences of the regularity
axiom. In the second part we introduce the successor of a set and the notions
of transitivity and connectedness wrt membership relation. Then we define
ordinal numbers as transitive and connected sets, and we prove some theorems
of them and of their sets. Lastly we introduce the concept of a transfinite
sequence and we show transfinite induction and schemes of defining by
transfinite induction.}}

