# The continuum of the surreal numbers revisited.The surreal numbers defined through transfinite Cauchy fundamental sequences

@inproceedings{Kyritsis2021TheCO, title={The continuum of the surreal numbers revisited.The surreal numbers defined through transfinite Cauchy fundamental sequences}, author={Konstantinos Kyritsis}, year={2021} }

In this treatise on the theory of the continuum of the surreal numbers of J.H. Conway, is proved ,that the three different techniques and hierarchies of the continuums of the transfinite real numbers of Glayzal A. (1937) defined through transfinite power series , of the surreal numbers of J.H. Conway (1976) defined by Dedekind cuts ,and of the ordinal real numbers of K. E. Kyritsis (1992) defined by fundamental Cauchy transfinite sequences, give by inductive limit or union the same class and…

## References

SHOWING 1-10 OF 10 REFERENCES

The universality of formal power series fields

- Mathematics
- 1939

In a recent paper,f André Gleyzal has constructed ordered fields consisting of certain "transfinite real numbers" and has established the interesting result that any ordered field can be considered…

Fourier Analysis on Groups

- Mathematics
- 1962

In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact…

Non-Standard Analysis

- Mathematics
- 1977

1. As early as 1934 it was pointed out by Thoralf Skolem (see [17]) that there exist proper extensions of the natural number system which have, in some sense, ‘the same properties’ as the natural…

Topology and Order Neumann B . H 1949 ] . On ordered division rings

- Transact . of the Amer . Math . Soc .
- 1976

Categories for the working mathematician Springer 1971 [ Monna A . F . 1970 ] Analyse non - Archimedienne Springer 1970

- 1971

Introduction to the theory of Infinitecimals Luxenburg W . A . J . 1976 ] N . Y . 1976 . [ Lynn A . Steen - Counterexamples in Toplogy Springer 1970

- Non - Standard analysis in topological algebra in Applications of Model Theory to Algebra , Analysis and Probability N . Y .
- 1969

Fractions of ordinal numbers Israel Institute of Tecnology Scient

- Public .
- 1955

The theory of valuastions

- Amer . Math . Soc .
- 1950

On an ordered algebraic field

- Warsow , Towarzytwo Nankowe Warzawskie
- 1948

. 1984 . [ Laugwitz Detler 1983 ] Ω Calculus as a Generalization of Field Extension . An alternative approach to non - Standard analysis " Recent developments in non - standard analysis