Working paper Open Access

Some steps towards a theory of expressions

Colignatus, Thomas


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    <subfield code="a">&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;</subfield>
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