Kazu to Ha Nani Ka Soshite Nande Arubeki Ka / Original Title: Stetigkeit Und Irrationale Zahlen Gentitle : Was Sind Und Was Sollen Die Zahlen? (Chiku Ma Gakugei Bunko Te 9-1 Math & Science)

[Machine Translation] Two monographs are included that are representative of Dedekind's work: "Continuity and Impossible Numbers," which attempts a rigorous foundation for real numbers based on the concept of "disconnection," and "What Are Numbers and What Should They Be? The monographs include two monographs that are representative of Dedekind's work: "What Are Numbers and What Should They Be? In addition, the translator's "Foundations of Mathematics from a Modern Perspective," which complements Dedekind's argument and includes the incompleteness theorem and the continuum hypothesis, is included as an appendix to the monographs by Emmy Neter and Ernst Zermelo. A long-awaited new translation of this long-read classic of mathematical theory!

「切断」の概念により実数の厳密な基礎付けを試みた『連続性と無理数』、そして数学的論理のみから自然数論を展開した『数とは何かそして何であるべきか?』の、デデキントの業績を代表する2篇のモノグラフを収録。付録としてエミー・ネーターとエルンスト・ツェルメロの論考に加え、デデキントの議論を補いつつ不完全性定理や連続体仮説までをも射程に入れた、訳者による「現代の視点からの数学の基礎付け」を収録。長く読み継がれてきた数学論の古典、待望の新訳!