Дедекинд, Юлиус Вильгельм Рихард цитаты

Ю́лиус Вильге́льм Ри́хард Дедеки́нд — немецкий математик, известный работами по общей алгебре и основаниям вещественных чисел. Wikipedia  

✵ 6. Октябрь 1831 – 12. Февраль 1916
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Дедекинд, Юлиус Вильгельм Рихард: Цитаты на английском языке

“The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes—which itself is nowhere carefully defined—and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself.”

Footnote: The apparent advantage of the generality of this definition of number disappears as soon as we consider complex numbers. According to my view, on the other hand, the notion of the ratio between two numbers of the same kind can be clearly developed only after the introduction of irrational numbers.
Stetigkeit und irrationale Zahlen (1872)