ORDINAL REAL NUMBERS 1. The ordinal characteristic
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Ημερομηνία
Συγγραφείς
Konstantinos E. Kyritsis
Τίτλος Εφημερίδας
Περιοδικό ISSN
Τίτλος τόμου
Εκδότης
Christow Frangos Volume: PROCEEDINGS: https://books.google.gr/books?id=BSUsDwAAQBAJ&pg
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full paper
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April 2017 Conference: 1ST INTERNATIONAL CONFERENCE ON QUANTITATIVE, SOCIAL, BIOMEDICAL AND ECONOMIC ISSUES 2017 - ICQSBEI 2017 ,ATHENS, GREECEAt: ATHENS, GREECE
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Όνομα βιβλίου
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Συμπληρωματικός/δευτερεύων τίτλος
Περιγραφή
In this paper are introduced the ordinal integers ,the ordinal rational numbers ,the ordinal real numbers ,the ordinal p-adic numbers ,the ordinal complex numbers and the ordinal quaternion numbers .It is also introduced the ordinal characteristic of linearly ordered fields. The final result of this series of papers shall be that the three different techniques of surreal numbers, of transfinite real numbers ,of ordinal real numbers give by inductive limit or union the same class of numbers known already as the class No and that would deserve the name the "infinitary totally ordered Newton-Leibniz realm of numbers ".The ordinal characteristic is essentially a measurement of the size of a linearly ordered commutative field with a semi-ring of Ordinal natural numbers (Hessenberg natural commutative operations in the ordinal numbers, as developed in the two previous papers-sections). We embed systems of ordinal natural numbers in a linearly ordered field, so that not “gaps” exist. There is always a minimal such system the natural numbers themselves. The definition of the ordinal characteristic of such ordinal natural numbers is always the supremum of the ordinals which are contained in it, and it is a principal ordinal numbers as we have described in the previous paper-section. Then we embed with monomorphisms and with 1-1 functions , such semi-rings of ordinal natural numbers in a linearly ordered commutative field so that the 0 and 1 of the ordinal real numbers goes to the 0, 1 of the linearly ordered field and there are no “gaps”, in other words the image is the minimal such possible set in the linearly ordered field. All such possible monomorphic with no gaps in a linearly ordered field, which is a set, give a set of corresponding ordinal characteristics of such semi-rings of ordinal natural numbers which is upper bounded, because of the cardinal and corresponding ordinal of the set and linearly ordered field. Thus as such ordinal are a subset of a well ordered set of ordinals it holds the supremum property, and there is such a supremum ordinal. Since also such a maximal embedding is also a semi-ring of ordinal natural numbers, this supremum is also a principal ordinal number which exist and its unique, it measures the size of the linearly ordered field and we call the it its ordinal characteristic. Having defined the ordinal characteristic as above the next definitions follow with minor corrections.
Περιγραφή
Λέξεις-κλειδιά
Hessenberg natural operations, transfinite real numbers, linearly ordered commutative fields, Surreal numbers
Θεματική κατηγορία
MATHEMATICS
Παραπομπή
Σύνδεσμος
Γλώσσα
en
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Γενική Περιγραφή / Σχόλια
Ίδρυμα και Σχολή/Τμήμα του υποβάλλοντος
University of Iannina, School of Economic and Administrative Sciences, Dept of Accouning-Finance
Πίνακας περιεχομένων
Χορηγός
Βιβλιογραφική αναφορά
April 2017 Conference: 1ST INTERNATIONAL CONFERENCE ON QUANTITATIVE, SOCIAL, BIOMEDICAL AND ECONOMIC ISSUES 2017 - ICQSBEI 2017 ,ATHENS, GREECEAt: ATHENS, GREECEVolume: PROCEEDINGS: https://books.google.gr/books?id=BSUsDwAAQBAJ&pg
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Άδεια χρήσης της εγγραφής: CC0 1.0 Universal