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The Two Couriers Problem and Diverse Approaches to Division by Zero
  • Budee U Zaman
Budee U Zaman
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Abstract

 In this paper, we delve into the historical and enduring algebraic conundrum known as the Two Couriers Problem, originally posed by the French mathematician Clairaut in 1746. Over the centuries, this problem has persisted, finding its way into numerous textbooks, journals, and mathematical discussions. One of the remarkable aspects of the Two Couriers Problem is its inherent connection to division by zero, a mathematical operation that has intrigued scholars for generations. Division by zero, a concept laden with complexity and ambiguity, has sparked diverse mathematical approaches. Conventional mathematics regards division by zero as an indeterminate or undefined result. However, alternative methodologies have emerged over time. Transmathematics defines division by zero as either nullity or explicitly positive or negative infinity, offering a different perspective. Saitoh simplifies division by zero as zero, challenging traditional conventions, while Barukˇci´c explores the possibility of defining it as either unity or explicitly positive or implicitly negative infinity. Amidst these varied approaches, the central question persists: which method offers the most effective solution to the enigma of division by zero? To answer this question, we propose utilizing the Two Couriers Problem as an objective benchmark. By subjecting these different mathematical approaches to this historical problem, we aim to rigorously evaluate their efficacy and determine which one stands out as the most viable solution. This paper seeks to unravel the complexities of division by zero through a systematic analysis, utilizing the Two Couriers Problem as a guiding light. By doing so, we endeavor to shed new insights on this age-old mathematical puzzle and contribute valuable perspectives to the ongoing discourse surrounding division by zero and its diverse interpretationÂ