# Beiträge zur Begründung der transfiniten Mengenlehre

@article{CantorBeitrgeZB, title={Beitr{\"a}ge zur Begr{\"u}ndung der transfiniten Mengenlehre}, author={Georg Cantor}, journal={Mathematische Annalen}, volume={49}, pages={207-246} }

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## 411 Citations

Counterexamples to

- Mathematics, Philosophy

The Cantor-Schroeder-Bernstein theorem [Can97][Sch98][Ber05] states that any two sets that have injections into each other have the same cardinality, i.e. there is a bijection between them. Another…

The Concept of Existence in Mathematics El concepto de existencia en matemáticas

- Mathematics
- 2017

We assert that, from a pragmatic point of view, mathematicians treat mathematical objects as if they were real. If a theory is consistent, theorems are discovered (sometimes with analyses not…

2. Frege versus Cantor and Dedekind: On the Concept of Number

- Philosophy
- 1996

There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion…

ADDRESSING MATHEMATICAL INCONSISTENCY : CANTOR AND GÖDEL REFUTED

- Mathematics, Philosophy
- 2010

This article undertakes a critical reappraisal of arguments in support of Cantor's theory of transfinite numbers. The following results are reported: - Cantor's proofs of nondenumerability are…

CONWAY'S FIELD OF SURREAL NUMBERS

- Mathematics
- 1985

Conway introduced the Field No of numbers, which Knuth has called the surreal numbers. No is a proper class and a real-closed field, with a very high level of density, which can be described by…

DECIDING SOME UNDECIDABLE TOPOLOGICAL STATEMENTS *

- Philosophy
- 1979

1 appreciate the kind introductory remarks and I am grateful also to Paul Meyer and the Organizing Committee for the invitation to be here; it is a pleasure and an honor to address the Academy. I…

On The History and Mathematics of The Equivalence Theorem

- Mathematics
- 2013

Trevor wrote three major histories, [62; 63; 64], as well as many mathematical papers in his multi-faceted career and it is a great pleasure for me to dedicate to his memory this offering on the…

Generosity: No Doubt, but at Times Excessive and Delusive

- Mathematics
- 2007

AbstractOne of the ways in which the artificial languages of mathematics are “generous”, that is, in which they assists the advance of thought, is through its establishment of advanced operatory…

CO-PARTIAL FUNCTIONS : A STEP TOO FAR ?

- Philosophy
- 2012

Mathematicians interested in computability theory have to deal with partial functions. Those interested in the theory of complex variables talk of multi-valued functions. Even in elementary…

Construction of the Transreal Numbers and Algebraic Transfields

- Mathematics
- 2015

The transreal numbers, introduced by James Anderson, are an extension of the real numbers. The four arithmetical operations of addition, subtraction, multiplication and division are closed on the set…