“The above comparison of the domain R of rational numbers with a straight line has led to the recognition of the existence of gaps, of a certain incompleteness or discontinuity of the former, while we ascribe to the straight line completeness, absence of gaps, or continuity. In what then does this continuity consist? Everything must depend on the answer to this question, and only through it shall we obtain a scientific basis for the investigation of all continuous domains.”

— Richard Dedekind

p, 125
Stetigkeit und irrationale Zahlen (1872)

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Richard Dedekind 13

German mathematician 1831–1916

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