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

## Monoid of Multisets and Subsets

Grzegorz Bancerek
Polish Academy of Sciences, Institute of Mathematics, Warsaw

### Summary.

The monoid of functions yielding elements of a group is introduced. The monoid of multisets over a set is constructed as such monoid where the target group is the group of natural numbers with addition. Moreover, the generalization of group operation onto the operation on subsets is present. That generalization is used to introduce the group \$2^G\$ of subsets of a group \$G\$.

#### MML Identifier: MONOID_1

The terminology and notation used in this paper have been introduced in the following articles [17] [10] [21] [20] [2] [22] [8] [5] [4] [9] [7] [14] [16] [12] [19] [6] [11] [1] [18] [3] [13] [15]

#### Contents (PDF format)

1. Updating
2. Monoid of functions into a semigroup
3. Monoid of multisets over a set
4. Monoid of subsets of a semigroup

#### Bibliography

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