Portal de Periódicos da CAPES

The Integers

1998; Linguagem: Inglês

10.1007/978-1-4471-0425-4_2

2197-4144

D. A. R. Wallace,

Numbers are encountered early in life and in many practical contexts. In our infancy we develop a feeling for the natural numbers by chanting "one, two, three, …", "eins, zwei, drei, …", "yî, èr, sân,…", or their equivalent, in whatever may be our mother tongue. By childhood we have assimilated, without too much conscious effort, the elementary properties of the addition, subtraction, multiplication and division of the natural numbers; in this text we take these elementary properties for granted. In such an approach we are following the celebrated dictum of L. Kronecker (1823–91), namely, "Die ganze Zahl schuf der liebe Gott; alles übrige ist Menschenwerk" which we may render in English as "God created the integers; everything else is man's handiwork". (Quotation from Philosophie der Mathematik und Naturwissenschaft by H. Weyl, R. Oldenburg, München, 1928, Section 6, page 27).