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

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.