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En lógica y matemáticas, los axiomas de Zermelo-Fraenkel, formulados por Ernst Zermelo y Adolf Fraenkel, son un sistema axiomático concebido para formular la teoría de conjuntos. Normalmente se abrevian como ZF o en su forma más común, complementados por el axioma de elección ( axiom of C hoice ), como ZFC .
Zermelo–Fraenkel set theory. In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
The most widely used and accepted set theory is known as ZFC, which consists of Zermelo–Fraenkel set theory including the axiom of choice (AC). The links show where the axioms of Zermelo's theory correspond.
In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of Zermelo–Fraenkel set theory. It guarantees the existence of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908.
En lógica y matemáticas, los axiomas de Zermelo-Fraenkel, formulados por Ernst Zermelo y Adolf Fraenkel, son un sistema axiomático concebido para formular la teoría de conjuntos. Normalmente se abrevian como ZF o en su forma más común, complementados por el axioma de elección, como ZFC.
2 de jul. de 2013 · The four central axioms of Zermelo's system are the Axioms of Infinity and Power Set, which together show the existence of uncountable sets, the Axiom of Choice, to which we will devote some space below, and the Axiom of Separation.
In axiomatic set theory, the axiom of union is one of the axioms of Zermelo–Fraenkel set theory. This axiom was introduced by Ernst Zermelo. Informally, the axiom states that for each set x there is a set y whose elements are precisely the elements of the elements of x.
