*Numbers are “things in themselves”Wittgenstein, I believe, was the one who proposed the human inability to communicate with lions, should we give the regal beasts the ability to speak our language.*

*Numbers are “things in themselves”Wittgenstein, I believe, was the one who proposed the human inability to communicate with lions, should we give the regal beasts the ability to speak our language.This has everything to do with context, perspective, understandings, and connections. Review: Richard Dedekind, Essays on the Theory of Numbers: I. *

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.

The translation is rather painfully literal, and does not convey much idea of the graceful style of the original; but it is, on the whole, correct.

It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.

The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had be This volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers.

), dove con un anno di anticipo su Peano fornisce una descrizione assiomatica dei numeri naturali.

Curiosità: per lui l'induzione matematica è un teorema, perché usa come assioma la possibilità di avere catene infinite di insiemi.

This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.

The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times.

It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.

The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system.

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