Colignatus, Thomas
2015-07-26
<p><em><strong>Foundations of Mathematics. A Neoclassical Approach to Infinity </strong></em>is for (1) students interested in methodology and the foundations of mathematics – e.g. studying physics, engineering, economics, psychology, thus a broad group who use mathematics – and (2) teachers of mathematics who are sympathetic to the idea of bringing set theory and number theory into mathematics education.</p>
<p>The book presents:<br>
(A) Constructivism with Abstraction, as a methodology of science.<br>
(B) Particulars about infinity and number theory, within foundations and set theory.<br>
(C) Correction of errors within mathematics on (B), caused by neglect of (A).</p>
<p>Other readers are (3) research mathematicians, who would benefit from last correction, but who must mend for that they are not in the prime target groups.</p>
<p>Set theory and number theory would be important for a better educational programme:<br>
(i) They greatly enhance competence and confidence.<br>
(ii) They open up the mind to logical structure and calculation also in other subjects.<br>
(iii) They are fundamental for learning and teaching themselves.</p>
<p>The axiomatic system for set theory ZFC is shown to be inconsistent. Mathematics has been in error since Cantor 1874 because of neglecting above methodology of science.</p>
ISBN 978 94 625422-0-4. The book website is: http://thomascool.eu/Papers/FMNAI/Index.html
https://doi.org/10.5281/zenodo.291982
oai:zenodo.org:291982
Zenodo
https://doi.org/10.5281/zenodo.291848
https://doi.org/10.5281/zenodo.291974
https://zenodo.org/communities/re-engineering-math-ed
https://doi.org/
info:eu-repo/semantics/openAccess
Creative Commons Attribution Non Commercial No Derivatives 4.0 International
https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
foundations of mathematics, infinity, Cantor, Occam, diagonal argument, ZFC, consistency, neoclassical approach, bijection by abstraction, Paul of Venice, education, didactics, re-engineering
Foundations of Mathematics. A Neoclassical Approach to Infinity
info:eu-repo/semantics/book