Dedekind Richard. Essays On The Theory Of Numbers Essays On Heterosexism
Richard Dedekind (1831 - 1916) was one of the pioneers of number theory and this book contains the English translations of his two most important papers: “Continuity and Irrational Numbers” from 1872 and “The Nature and Meaning of Numbers” from 1887.
The first paper shows how he came up with a purely number based procedure that defined the inexact irrational numbers like square root of 2.
His procedure, now called the Dedekind cut, was based upon the right triangle formula in which summing the sq Richard Dedekind (1831 - 1916) was one of the pioneers of number theory and this book contains the English translations of his two most important papers: “Continuity and Irrational Numbers” from 1872 and “The Nature and Meaning of Numbers” from 1887.
Since then number theorists / logicians have tried to come up with context based logics to axiomatize number theory, apparently without success. One contains the original presentation of the famous "Dedekind cut" formulation of the real numbers, plus developments up to the well-known "sup" property of bounded sets of reals.
Dedekind gives a theory of irrational numbers and of the arithmetical continuum which is logically perfect, and in form, perhaps, more simple and direct than any other which has been or could be suggested; in the second he proceeds, by a marvellous chain of subtle inferences, from the idea of a manifold (or system of distinguishable objects in the widest sense) to the series of natural numbers and the elementary operations of arithmetic.
It is to be hoped that the translation will make the essays better known to English mathematicians; they are of the very first importance, and rank with the work of Weierstrass, Kronecker and Cantor in the same field. 15, “hereafter” is a wrong rendering of hierauf; on p.
But this was mathematical theory, and it was fascinating to see a math narrative and vocabulary at work..though I didn't get it.
As Dedekind attempts to "investigate our notions of space and time by bringing them into relation with this number odoain created in our mind, I simply say, do or do not... I just wanted to ride along for a second and see how this half lived.