Working paper Open Access
Colignatus, Thomas
<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://datacite.org/schema/kernel-4" xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4.1/metadata.xsd"> <identifier identifierType="DOI">10.5281/zenodo.346001</identifier> <creators> <creator> <creatorName>Colignatus, Thomas</creatorName> <givenName>Thomas</givenName> <familyName>Colignatus</familyName> <affiliation>Samuel van Houten Genootschap</affiliation> </creator> </creators> <titles> <title>Some steps towards a theory of expressions</title> </titles> <publisher>Zenodo</publisher> <publicationYear>2017</publicationYear> <subjects> <subject>Expression, fraction, syntax, semantics, substitution, numerator, denominator, H, computer algebra, Mathematica, mathematics education</subject> </subjects> <dates> <date dateType="Issued">2017-03-06</date> </dates> <resourceType resourceTypeGeneral="Text">Working paper</resourceType> <alternateIdentifiers> <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/346001</alternateIdentifier> </alternateIdentifiers> <relatedIdentifiers> <relatedIdentifier relatedIdentifierType="DOI" relationType="References">10.5281/zenodo.291979</relatedIdentifier> <relatedIdentifier relatedIdentifierType="DOI" relationType="References">10.5281/zenodo.292244</relatedIdentifier> <relatedIdentifier relatedIdentifierType="DOI" relationType="References">10.5281/zenodo.292247</relatedIdentifier> <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://zenodo.org/communities/re-engineering-math-ed</relatedIdentifier> </relatedIdentifiers> <rightsList> <rights rightsURI="http://creativecommons.org/licenses/by-nc-nd/4.0/legalcode">Creative Commons Attribution Non Commercial No Derivatives 4.0 International</rights> <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights> </rightsList> <descriptions> <description descriptionType="Abstract"><p>The mathematical "theory of expressions" better be developed in a general fashion, so that it can be referred to in various applications. The paper discusses an example when there is a confusion between syntax (unevaluated) and semantics (evaluated), when substitution causes a contradiction. However, education should not wait till such a mathematical theory of expressions is fully developed. Computer algebra is sufficiently developed to support and clarify these issues. Fractions <em>y</em> / <em>x</em> can actually be abolised and replaced with <em>y</em> <em>x</em><sup><em>H</em></sup> with <em>H</em> = -1 as a constant like exponential number <em>e</em> or imaginary number <em>i</em>.</p></description> </descriptions> </resource>
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