Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989 Association of Mizar Users

## Functions from a Set to a Set

Czeslaw Bylinski
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.

### Summary.

The article is a continuation of [1]. We define the following concepts: a function from a set \$X\$ into a set \$Y\$, denoted by ``Function of \$X\$,\$Y\$'', the set of all functions from a set \$X\$ into a set \$Y\$, denoted by Funcs(\$X\$,\$Y\$), and the permutation of a set (mode Permutation of \$X\$, where \$X\$ is a set). Theorems and schemes included in the article are reformulations of the theorems of [1] in the new terminology. Also some basic facts about functions of two variables are proved.

#### MML Identifier: FUNCT_2

The terminology and notation used in this paper have been introduced in the following articles [4] [3] [5] [6] [7] [1] [2]

#### Contents (PDF format)

1. Functions from a set to a set
2. Partial functions from a set to a set (from \cite{PARTFUN1.ABS})

#### Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[4] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[5] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[6] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[7] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.