10.5281/zenodo.346001
https://zenodo.org/records/346001
oai:zenodo.org:346001
Colignatus, Thomas
Thomas
Colignatus
Samuel van Houten Genootschap
Some steps towards a theory of expressions
Zenodo
2017
Expression, fraction, syntax, semantics, substitution, numerator, denominator, H, computer algebra, Mathematica, mathematics education
2017-03-06
Working paper
10.5281/zenodo.291979
10.5281/zenodo.292244
10.5281/zenodo.292247
https://zenodo.org/communities/re-engineering-math-ed
Creative Commons Attribution Non Commercial No Derivatives 4.0 International
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 y / x can actually be abolised and replaced with y xH with H = -1 as a constant like exponential number e or imaginary number i.