Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Increasing and Continuous Ordinal Sequences

Grzegorz Bancerek

Warsaw University, Bialystok
Summary.

Concatenation of two ordinal sequences,
the mode of all ordinals belonging to a universe and
the mode of sequences of them with length equal to the rank of
the universe are introduced.
Besides,
the increasing and continuous transfinite sequences,
the limes of ordinal sequences and
the power of ordinals, and
the fact that every increasing and continuous transfinite sequence has
critical numbers (fixed points) are discussed.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[5]
[8]
[9]
[4]
[1]
[2]
[3]
[6]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
Ordinal arithmetics.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Bogdan Nowak and Grzegorz Bancerek.
Universal classes.
Journal of Formalized Mathematics,
2, 1990.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received May 31, 1990
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