Due to the fact that their visual appeal within the overdue nineteenth century, the Cantor--Dedekind idea of actual numbers and philosophy of the continuum have emerged as pillars of ordinary mathematical philosophy. however, this era additionally witnessed the emergence of numerous substitute theories of genuine numbers and corresponding theories of continua, in addition to non-Archimedean geometry, non-standard research, and a couple of very important generalizations of the method of actual numbers, a few of which were defined as mathematics continua of 1 kind or one other.
aside from E.W. Hobson's essay, that's interested in the tips of Cantor and Dedekind and their reception on the flip of the century, the papers within the current assortment are both all for or are contributions to, the latter teams of reviews. all of the participants are amazing gurus of their respective fields, and the essays, that are directed to historians and philosophers of arithmetic in addition to to mathematicians who're considering the principles in their topic, are preceded via a long historic creation.
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