Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

Yatsuka Nakamura; Hisashi Ito

Formalized Mathematics (2008)

  • Volume: 16, Issue: 3, page 283-288
  • ISSN: 1426-2630

Abstract

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Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept came from the individual Ergodic theorem (see [7]) and it is the preparation for its proof.

How to cite

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Yatsuka Nakamura, and Hisashi Ito. "Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences." Formalized Mathematics 16.3 (2008): 283-288. <http://eudml.org/doc/266669>.

@article{YatsukaNakamura2008,
abstract = {Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept came from the individual Ergodic theorem (see [7]) and it is the preparation for its proof.},
author = {Yatsuka Nakamura, Hisashi Ito},
journal = {Formalized Mathematics},
language = {eng},
number = {3},
pages = {283-288},
title = {Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences},
url = {http://eudml.org/doc/266669},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Yatsuka Nakamura
AU - Hisashi Ito
TI - Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 3
SP - 283
EP - 288
AB - Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept came from the individual Ergodic theorem (see [7]) and it is the preparation for its proof.
LA - eng
UR - http://eudml.org/doc/266669
ER -

References

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  1. [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
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  7. [7] Paul R. Halmos. Lectures on Ergodic Theory. The Mathematical Society of Japan, 1956. No.3. Zbl0073.09302
  8. [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  9. [9] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  10. [10] Karol Pαk. Cardinal numbers and finite sets. Formalized Mathematics, 13(3):399-406, 2005. 
  11. [11] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  12. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  13. [13] Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001. 
  14. [14] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 

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