Abstract
English translation of Moritz Pasch,“Begriffsbildung und Beweis in der Mathematik,” Annalen der Philosophie und philosophischen Kritik 4 (1925), pp. 348–367, 417–426. This paper consists of five independent essays. In “Proof and Definition in Mathematics,” Pasch analyzes the notion of direct proof . In “Equality in Mathematics,” he explains why “equals” in mathematics is best understood as “is identical to.” In “The Decidability Requirement in Mathematics,” he offers examples of decidable and undecidable properties and concludes that we cannot understand the logical structure of mathematics without clearly distinguishing between the two. In “Approximations of Arbitrary Numbers; the Indefinite Infinite,” he provides an implicit definition of the “indefinite infinite,” an infinite number that is neither positive nor negative and neither greater nor less than any real number . “The Imaginary in Mathematics” is a semi-popular introduction to complex numbers.
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