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Building the Logarithm: A Visual Proof With The Least Upper Bound
Автор: Rigorous Motion
Загружено: 2026-01-11
Просмотров: 98
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We build the logarithm function from scratch using the tools of real analysis. Starting with basic integer powers, we use the Least Upper Bound property to fill the gaps in the number line. This proof demonstrates exactly why logarithms exist and guarantees that for every base b and target y, there is a unique exponent x that solves the equation. This is a step by step guide to constructing one of the most important functions in mathematics without taking shortcuts.
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