Meadow based Fracterm Theory
Jan A. Bergstra
TL;DR
The paper introduces fracterms as a new formal proxy for fractions within meadow theory, providing a precise framework that bridges the conceptual gap between fractions as values and as expressions.
Contribution
It formulates a rigorous definition of fracterms and explores their classes, offering a novel theoretical approach to understanding fractions in meadow of rational numbers.
Findings
Defined fracterms and their classes.
Provided a formal framework for fractions as fracterms.
Bridged the conceptual gap between fractions as values and expressions.
Abstract
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers viewing fractions as fracterms provides an adequate theory of fractions. A very different view on fractions is that fractions are values, i.e. rational numbers. Fracterms are used to provide a range of intermediate definitions between these two definitions of fractions
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Taxonomy
TopicsData Visualization and Analytics · Philosophy and History of Science · Algorithms and Data Compression