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In 1877 Georg Cantor (1845–1918) discovered to his own amazement that the points of a unit line segment can be put into one-one correspondence with the points of a unit square or more generally with the points of a ρ-dimensional cube. This counterintuitive result at first sight called into question the concept of dimension. Was it well-defined or even meaningful in mathematics? Cantor’s discovery marks the origin of the most important modern mathematical problem of dimension, the problem of its invariance.

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Cantor and Dedekind: Discovery of a Counterintuitive Example concerning Dimension

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  • 发表日期：

    2025年

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  • Dale Martin Johnson

摘要

In 1877 Georg Cantor (1845–1918) discovered to his own amazement that the points of a unit line segment can be put into one-one correspondence with the points of a unit square or more generally with the points of a ρ-dimensional cube. This counterintuitive result at first sight called into question the concept of dimension. Was it well-defined or even meaningful in mathematics? Cantor’s discovery marks the origin of the most important modern mathematical problem of dimension, the problem of its invariance.