Cardinality of the sets of all bijections, injections and surjections

• Autorzy: Marcin Zieliński

Warianty tytułu

PL

Cardinality of the sets of all bijections, injections and surjections

• Języki publikacji: EN

Abstrakty

PL

The results of Zarzycki for the cardinality of the sets of all bijections, surjections, and injections are generalized to the case when the domains and codomains are infinite and different. The elementary proofs the cardinality of the sets of bijections and surjections are given within the framework of the Zermelo-Fraenkel set theory with the axiom of choice. The case of the set of all injections is considered in detail and more explicit an expression is obtained when the Generalized Continuum Hypothesis is assumed.

• Wydawca: Wydawnictwo Naukowe Uniwersytetu Pedagogicznego
• Czasopismo: Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
• Rocznik: 2019
• Tom: 11
• Strony: 143-151

Daty

wydano

2020-02-05

Twórcy

autor

Marcin Zieliński

Identyfikatory

DOI

10.24917/20809751.11.8