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The Search for Mathematical Roots, 1870-1940 by I. Grattan-Guinness

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CHAPTER 3

Cantor: Mathematics as Mengenlehre

3.1 PREFACES

3.1.1 Plan of the chapter. After summarising Cantor’s life and career in the next section, the story is told of his creation of the branch of mathematics which we call ‘set theory’; but when I wish to refer to his version of it I shall conserve even in translations the word ‘Mengenlehre’ which he used especially in his final years of the mid 1890s and which became the most common name among German-writing authors there after (§4.2.1). First, §3.2–3 covers its founding between 1870 and 1885, and §3.4 treats the final papers. Important concurrent work of Dedekind is also included: on irrational numbers in §3.2.4, and on integers in §3.4.1–3. Then §3.5 presents a survey of some of the main ...

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