Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992 Association of Mizar Users

## Sum and Product of Finite Sequences of Elements of a Field

Warsaw University, Bialystok

### Summary.

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.

#### MML Identifier: FVSUM_1

The terminology and notation used in this paper have been introduced in the following articles [18] [22] [19] [2] [23] [5] [7] [6] [3] [4] [16] [21] [17] [9] [8] [10] [15] [14] [1] [12] [20] [13]

#### Contents (PDF format)

1. Auxiliary theorems
2. Some operations on \$i\$-tuples
3. The sum of finite number of elements
4. The product of finite number of elements
5. The product of vectors

#### Acknowledgments

I would like to thank Czes{\l}aw Byli\'nski for his help.

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