Definições de conjunto finito
AUTOR(ES)
Frank Thomas Sautter
DATA DE PUBLICAÇÃO
1995
RESUMO
We analize Dedekind s (1893), ZermeIo s (1908) and Alarcón Athens (1987) definitions of finite sets. From these definitions we formulate and prove some mathematical induction principles for finite sets. We obtain a new definition of finite sets: a set C is finite if and only if the empty set beIongs to every non-empty famiIy F of subsets of C, such that for every non-empty set D PERTENCE F there exists exactly one set E PERTENCE F such that E = D - {d} for some d PERTENCE D. We prove that, in ZermeIo-Fraenkel axiomatics without the choice axiom, this definition is formally equivalent to Dedekind s axiom, which says that every infinite set, in the ordinary sense, has an enumerabIe subset.
ASSUNTO(S)
teoria axiomatica dos conjuntos logica simbolica e matematica
