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From Historically First "Unary" Numbers, Through Egyptian Fractions, Roman Numerals, Leibniz's Binary Numbers And Kepler's Fractions To Modern Ideas Such As Calkin-Wilf Tree: A Unified Approach To Representing Natural Numbers And Fractions, Olga Kosheleva, Vladik Kreinovich, Christian Servin

Departmental Technical Reports (CS)

In elementary mathematics classes, students are often overwhelmed by different representations of numbers and corresponding operations: usual fractions, decimal representations, binary numbers, etc. What often helps is when students learn the history of these representations, see the limitations of seemingly reasonable representations like Roman numerals, and how other representations overcame these limitations. Still, history was developed somewhat randomly, so the historical sequence is still somewhat chaotic. We believe that providing a unified approach for all these representations would help describe their sequence in a more logical way and thus, help the students even more.

In our analysis, we explore the …