The Infinite in Mathematics pp 114-150 | Cite as

# Set Theory

Chapter

## Abstract

Our results to date give us the tools for analysing the main concepts of set theory, the mathematical theory of the infinitely large. What is important for this task is above all to distinguish between individual and specific universality, to eliminate the concept of a set in defining natural numbers, to grasp the connection between cardinal and ordinal number, to acknowledge the result of analysing the principle of complete induction and to dissolve the symbolism of irrational numbers.

## Keywords

Ordinal Number Cardinal Number Decimal Fraction Diagonal Procedure Infinite Totality
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## Notes

- 6.An excellent account of the various definitions of finitude is given by A. Tarski, ‘Sur les ensembles finis’,
*Fundamenta Mathematica*6 (1925). 45–95.Google Scholar - 9.Letter to Bernouilli. Mathematische Schriften (edited by Gerhardt), III, p. 533.Google Scholar
- 25.A Theorem Concerning the Infinite Cardinal Numbers’,
*Quart. Journ. of Pure and Applied Math.*35 (1903), 87–94.Google Scholar - 26.Beweis, dassjede Menge wohlgeordnet werden kann’,
*Math. Ann*. 59 (1904), 514–516; ‘Neuer Beweis für die Wohlordnung’, ibid., 65 (1908), 107–128.Google Scholar - 33.Über Möglichkeiten im Relativkalkül’,
*Math. Ann.*76 (1915), 447–470.CrossRefGoogle Scholar

## Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978