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27 de abr. de 2024 · While their thinking was primarily governed by concepts vis-à-vis calculations, they were perfectly capable of and did perform difficult calculations. Besides, calculations involve concepts and lead to new concepts, as they did in the case of Abel, or Leopold Kronecker, who insisted on their primary role in mathematics.
27 de abr. de 2024 · The strongest criticism was voiced by the highly influential Leopold Kronecker who was defending the traditional finitism, that is, the view that only finite objects really exist. Cantor claimed that his infinite numbers are of the same nature as the irrational numbers, since both kinds of numbers are the limits of infinite sequences.
27 de abr. de 2024 · The working philosophy of mathematics this chapter considers, under the heading of “mathematical practice as philosophy,” is, analogously, that of the invention of new mathematical concepts. Against the grain of Deleuze and Guattari’s argument, mathematical concepts will be understood here in affinity with rather than in juxtaposition to ...
27 de abr. de 2024 · Methods already familiar to Leopold Kronecker allow PA to interpret the integers ℤ, rational numbers ℚ, and even algebraic numbers \( \mathbbm{A} \). The algebraic numbers A are all the real or complex roots of polynomials with integer coefficients. Finite lists of numbers can be expressed in PA.
