The Principle of Consistent Finitisation of the Infinite

Postgraduate Thesis uoadl:2919843 185 Read counter

Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
2020-07-17
Year:
2020
Author:
Pisimisi Angeliki
Supervisors info:
Στυλιανός Νεγρεπόντης, Ομότιμος Καθηγητής, Σχολή Θετικών Επιστημών, Τμήμα Μαθηματικών, ΕΚΠΑ
Βασιλική Φαρμάκη, Καθηγήτρια, Σχολή Θετικών Επιστημών, Τμήμα Μαθηματικών, ΕΚΠΑ
Μιχαήλ Ανούσης, Καθηγητής, Τμήμα Μαθηματικών, Πανεπιστήμιο Αιγαίου
Original Title:
Η Αρχή της Συμβατής Περάτωσης του Απείρου
Languages:
Greek
Translated title:
The Principle of Consistent Finitisation of the Infinite
Summary:
The main subject of this thesis is the so-called Principle of Consistent Finitisation of the Infinite, which is presented in detail in Negrepontis - Farmaki' s paper entitled: The Principle of Consistent Finitisation of the Infinite and its paradoxical power. We study this Principle in detail in Chapter 1. In the following 4 Chapters, we study the impressive value of four axioms in four different branches of mathematics. We present arguments that each one of these axioms is a consistent finitisation of the infinite and we study the way in which the above branches of mathematics, as well as the specific axioms, are presented in the school books (Gymnasium and Lyceum).
We deal with:
The Least Principle and its role in Number Theory.
The 5th Postulate and its role in basic Euclidean Geometry.
The Principle of Eudoxus - Archimedes and its role in the theory of ratios of magnitudes
The Completeness property and its role in Mathematical Analysis.
In the last Chapter we present a long-term program of reversing the decline of mathematics education, which sets three goals.
Main subject category:
Science
Keywords:
consistent finitisation of Infinite, the Least Principle, the fifth Postulate, Eudoxus-Archimedes principle, the Completeness property
Index:
No
Number of index pages:
0
Contains images:
Yes
Number of references:
70
Number of pages:
362
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