## Finite Sequences and Tuples of Elements of a Non-empty Sets (1990)

Citations: | 295 - 7 self |

### BibTeX

@MISC{Bylinski90finitesequences,

author = {Czeslaw Bylinski},

title = {Finite Sequences and Tuples of Elements of a Non-empty Sets},

year = {1990}

}

### Years of Citing Articles

### OpenURL

### Abstract

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

### Citations

1278 | Tarski Grothendieck set theory
- Trybulec
- 1990
(Show Context)
Citation Context ...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. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles =-=[13]-=-, [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j... |

1257 | Functions and their basic properties
- Byliński
- 1990
(Show Context)
Citation Context ...sic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], =-=[6]-=-, [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b, x, x... |

1187 | Properties of subsets
- Trybulec
- 1990
(Show Context)
Citation Context ...t is denoted by element of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], =-=[16]-=-, [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural n... |

1012 | Functions from a set to a set
- Byliński
- 1990
(Show Context)
Citation Context ...about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], =-=[7]-=-, [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b, x, x1, x2, x3 ... |

988 | Relations and their basic properties
- Woronowicz
- 1990
(Show Context)
Citation Context ...ome basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], =-=[17]-=-, [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b,... |

725 | Some basic properties of sets
- Byliński
- 1990
(Show Context)
Citation Context ...and it is denoted by element of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], =-=[9]-=-, [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are nat... |

642 | The fundamental properties of natural numbers
- Bancerek
- 1990
(Show Context)
Citation Context ... n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], =-=[1]-=-, [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural numb... |

634 | The ordinal numbers
- Bancerek
- 1990
(Show Context)
Citation Context ...enoted by element of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], =-=[2]-=-, [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural number... |

551 | Basic properties of real numbers - Hryniewiecki - 1990 |

432 | Partial functions
- Byliński
- 1990
(Show Context)
Citation Context ...acts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], =-=[8]-=-, [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b, x, x1, x2... |

370 |
Subsets of real numbers
- Trybulec
(Show Context)
Citation Context ...element of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], =-=[14]-=-, [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a n... |

331 | Binary operations
- Byliński
- 1990
(Show Context)
Citation Context ...es of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], =-=[5]-=-, and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b, x, x1, x2, x3 are sets, ... |

292 | Domains and their Cartesian products
- Trybulec
- 1990
(Show Context)
Citation Context ...t of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], =-=[11]-=-, [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural... |

258 | Binary operations applied to functions
- Trybulec
- 1990
(Show Context)
Citation Context ...on-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and =-=[10]-=- provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A, a, b, x, x1, x2, x3 are sets, D, D ′ , E... |

174 | Enumerated sets
- Trybulec
- 1990
(Show Context)
Citation Context ...set D and it is denoted by element of D n . Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], =-=[12]-=-, [9], [16], [2], [3], [14], [11], [1], [15], [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l ar... |

113 | Basic functions and operations on functions - Byliński - 1990 |

85 |
Andrzej Trybulec and Czesław Byliński. Some properties of real numbers operations
- min, square, et al.
- 1989
(Show Context)
Citation Context ...Also some basic facts about tuples of a non-empty set are proved. MML Identifier: FINSEQ_2. WWW: http://mizar.org/JFM/Vol2/finseq_2.html The articles [13], [12], [9], [16], [2], [3], [14], [11], [1], =-=[15]-=-, [17], [6], [8], [7], [4], [5], and [10] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, l are natural numbers, k is a natural number, A,... |

26 | Andrzej Trybulec and Czes�law Byliński. Some properties of real numbers operations - min, square, et al. - 1989 |