@MISC{ORDINAL2.MIZ,
  AUTHOR = {Bancerek, Grzegorz},
  TITLE = {Sequences of Ordinal Numbers},
  SUBTITLE = {Beginnings of Ordinal Arithmetics},
  DAY = {18},
  MONTH = {July},
  YEAR = {1989},
  ADDRESS1 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {  In the first part of the article we introduce the following operations:
On $X$ that yields the set of all ordinals which belong to the set $X$,
Lim $X$ that yields the set of all limit ordinals which belong to $X$, and
inf $X$ and sup $X$ that yield the minimal ordinal belonging to $X$ and
the minimal ordinal greater than all ordinals belonging to $X$, respectively.
  The second part of the article starts with schemes that can be used to justify
the correctness of definitions based on the transfinite induction
(see \cite{ORDINAL1.ABS} or \cite{KURAT-MOST:1}). The schemes
are used to define addition, product and power of ordinal numbers. The
operations of limes inferior and limes superior of sequences of ordinals are
defined and the concepts of limit of ordinal sequence and increasing and
continuous sequence are introduced.}}

