Considering that their visual appeal within the overdue nineteenth century, the Cantor--Dedekind idea of genuine numbers and philosophy of the continuum have emerged as pillars of normal mathematical philosophy. nevertheless, this era additionally witnessed the emergence of numerous replacement theories of genuine numbers and corresponding theories of continua, in addition to non-Archimedean geometry, non-standard research, and a few very important generalizations of the approach of genuine numbers, a few of which were defined as mathematics continua of 1 variety or one other.
apart from E.W. Hobson's essay, that is serious about the guidelines of Cantor and Dedekind and their reception on the flip of the century, the papers within the current assortment are both all in favour of or are contributions to, the latter teams of experiences. all of the individuals are awesome experts of their respective fields, and the essays, that are directed to historians and philosophers of arithmetic in addition to to mathematicians who're thinking about the rules in their topic, are preceded through a long historic advent.
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