Volume 4, 1992

University of Bialystok

Copyright (c) 1992 Association of Mizar Users

**Katarzyna Zawadzka**- Warsaw University, Bialystok

- This article is concerned with a generalization of concepts introduced in [11], i.e., there are introduced the sum and the product of finite number of elements of any field. Moreover, the product of vectors which yields a vector is introduced. According to [11], some operations on $i$-tuples of elements of field are introduced: addition, subtraction, and complement. Some properties of the sum and the product of finite number of elements of a field are present.

- Auxiliary theorems
- Some operations on $i$-tuples
- The sum of finite number of elements
- The product of finite number of elements
- The product of vectors

- [1]
Grzegorz Bancerek.
Cardinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Grzegorz Bancerek and Krzysztof Hryniewiecki.
Segments of natural numbers and finite sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Binary operations.
*Journal of Formalized Mathematics*, 1, 1989. - [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.
Partial functions.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Czeslaw Bylinski.
Binary operations applied to finite sequences.
*Journal of Formalized Mathematics*, 2, 1990. - [9]
Czeslaw Bylinski.
Finite sequences and tuples of elements of a non-empty sets.
*Journal of Formalized Mathematics*, 2, 1990. - [10]
Czeslaw Bylinski.
Semigroup operations on finite subsets.
*Journal of Formalized Mathematics*, 2, 1990. - [11]
Czeslaw Bylinski.
The sum and product of finite sequences of real numbers.
*Journal of Formalized Mathematics*, 2, 1990. - [12]
Agata Darmochwal.
Finite sets.
*Journal of Formalized Mathematics*, 1, 1989. - [13]
Katarzyna Jankowska.
Transpose matrices and groups of permutations.
*Journal of Formalized Mathematics*, 4, 1992. - [14]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
*Journal of Formalized Mathematics*, 1, 1989. - [15]
Michal Muzalewski and Wojciech Skaba.
From loops to abelian multiplicative groups with zero.
*Journal of Formalized Mathematics*, 2, 1990. - [16]
Andrzej Trybulec.
Binary operations applied to functions.
*Journal of Formalized Mathematics*, 1, 1989. - [17]
Andrzej Trybulec.
Semilattice operations on finite subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [19]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [20]
Andrzej Trybulec and Agata Darmochwal.
Boolean domains.
*Journal of Formalized Mathematics*, 1, 1989. - [21]
Wojciech A. Trybulec.
Vectors in real linear space.
*Journal of Formalized Mathematics*, 1, 1989. - [22]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [23]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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