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18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind] |
Full Idea: Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power. | |
From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |
A reaction: Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects. |