Partial Functions

Czeslaw Bylinski

Warsaw University, Bialystok

Supported by RPBP.III-24.C1.

Summary.

In the article we define partial functions. We also define the following notions related to partial functions and functions themselves: the empty function, the restriction of a function to a partial function from a set into a set, the set of all partial functions from a set into a set, the total functions, the relation of tolerance of two functions and the set of all total functions which are tolerated by a partial function. Some simple propositions related to the introduced notions are proved. In the beginning of this article we prove some auxiliary theorems and schemes related to the articles: [1] and [2].

MML Identifier: PARTFUN1

Contents (PDF format)

1. Main Part
2. Appendix

Bibliography

[1] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Functions from a set to a set. 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.