Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
K\"onig's Theorem

Grzegorz Bancerek

Warsaw University, Bialystok
Summary.

In the article the sum and product of any number of cardinals are introduced
and their relationships to addition, multiplication and
to other concepts are shown. Then the K\"onig's theorem is proved.
The theorem that the cardinal of union of increasing family of sets
of power less than some cardinal {\bf m} is not greater than {\bf m},
is given too.
MML Identifier:
CARD_3
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[7]
[14]
[13]
[15]
[5]
[6]
[2]
[12]
[1]
[10]
[8]
[9]
[3]
[4]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
Cardinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Grzegorz Bancerek.
Cardinal arithmetics.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Grzegorz Bancerek.
Tarski's classes and ranks.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Andrzej Nedzusiak.
$\sigma$fields and probability.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received April 10, 1990
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