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Some steps towards a theory of expressions

Colignatus, Thomas


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  <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="https://creativecommons.org/licenses/by-nc-nd/4.0/">Creative Commons Attribution-NonCommercial-NoDerivatives</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;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 &lt;em&gt;y&lt;/em&gt; / &lt;em&gt;x&lt;/em&gt; can actually be abolised and replaced with &lt;em&gt;y&lt;/em&gt; &lt;em&gt;x&lt;/em&gt;&lt;sup&gt;&lt;em&gt;H&lt;/em&gt;&lt;/sup&gt; with &lt;em&gt;H&lt;/em&gt; = -1 as a constant like exponential number &lt;em&gt;e&lt;/em&gt; or imaginary number &lt;em&gt;i&lt;/em&gt;.&lt;/p&gt;</description>
  </descriptions>
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