The article explores Richard Dedekind's innovative concept of Dedekind cuts, which provided a rigorous foundation for the real number system by addressing the gaps within the rational numbers. It discusses how Dedekind's idea was to construct new numbers by defining cuts in rational numbers, enabling the resolution of previously unanswerable questions about irrational numbers without relying on infinite decimal expansions. The article highlights Dedekind's contribution to the evolution of mathematical thought and its impact on the development of set theory, as well as the broader implications for understanding numbers as constructions of the human mind.
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