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What advantage will be gained by even a purely abstract definition of real numbers of a higher type, I am as yet unable to see, conceiving as I do of the domain of real numbers as complete in itself.

— Richard Dedekind Stetigkeit und irrationale Zahlen (1872)

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If a, c are two different numbers, there are infinitely many different numbers lying between a, c.

Stetigkeit und irrationale Zahlen (1872)

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Quote text and notes from Wikiquote: Richard Dedekind (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.