Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Finite Sequences and
Tuples of Elements of a Non-empty Sets
-
Czeslaw Bylinski
-
Warsaw University, Bialystok
-
Supported by RPBP.III-24.C1.
Summary.
-
The first part of the article is a continuation of [4].
Next, we define the identity sequence of natural numbers
and the constant sequences. The main part of this article is the definition
of tuples. The element of a set of all sequences of
the length $n$ of $D$ is called a tuple of a non-empty set $D$
and it is denoted by element of $D^{n}$.
Also some basic facts about tuples of a non-empty set are proved.
The terminology and notation used in this paper have been
introduced in the following articles
[13]
[12]
[9]
[16]
[2]
[3]
[14]
[11]
[1]
[15]
[17]
[6]
[8]
[7]
[4]
[5]
[10]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
- [2]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [3]
Grzegorz Bancerek.
Sequences of ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
- [4]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
Journal of Formalized Mathematics,
1, 1989.
- [5]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Czeslaw Bylinski.
Partial functions.
Journal of Formalized Mathematics,
1, 1989.
- [9]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
- [10]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Andrzej Trybulec.
Enumerated sets.
Journal of Formalized Mathematics,
1, 1989.
- [13]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [14]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [15]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
- [16]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [17]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received March 1, 1990
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