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Sequences of Ordinal Numbers

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 [1] or [3]). 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 limet of ordinal sequence and increasing and continuous sequence are introduced.