What question did this study set out to answer?

This thesis aims to propose a consistent framework for understanding division by zero.

May 7, 2026Open Access

Defining division by zero

Key Points

This thesis aims to propose a consistent framework for understanding division by zero.
Examined the semantic implications of division by zero.
Proposed an alternative interpretation involving the complex plane.
Developed a logical framework for defining division by zero.
Identified semantic conflicts in existing definitions of division by zero.
Established a consistent framework equating division by zero with multiplication by zero.

Abstract

This short thesis reconciles the conflicting observations that arise from attempting to address division by zero in different ways, by proposing an alternative interpretation of the complex plane, and argues that the problem with defining division by zero is fundamentally semantic, arriving at a consistent framework in which division by zero is defined as equivalent to multiplication by zero.

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