Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996
Association of Mizar Users
Adjacency Concept for Pairs of Natural Numbers
-
Yatsuka Nakamura
-
Shinshu University, Nagano
-
Andrzej Trybulec
-
Warsaw University, Bialystok
Summary.
-
First, we introduce the concept of adjacency for a pair of natural numbers.
Second, we extend the concept for two pairs of natural numbers. The pairs
represent points of a lattice in a plane.
We show that if some property is infectious among adjacent points,
and some points have the property, then all points have the property.
MML Identifier:
GOBRD10
The terminology and notation used in this paper have been
introduced in the following articles
[9]
[4]
[12]
[10]
[1]
[7]
[13]
[3]
[2]
[5]
[11]
[6]
[8]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
Journal of Formalized Mathematics,
2, 1990.
- [6]
Katarzyna Jankowska.
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3, 1991.
- [7]
Takaya Nishiyama and Yasuho Mizuhara.
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5, 1993.
- [8]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
- [9]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [11]
Wojciech A. Trybulec.
Pigeon hole principle.
Journal of Formalized Mathematics,
2, 1990.
- [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 10, 1996
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