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008			220923b |||||||| |||| 00| 0 eng d
037			_cReference
040			_aRTL _cRTL _beng
041			_2eng _aeng
084			_aB13 K3/SC _qRTL
100			_aDedekind, Richard _9316876
245		0	_aEssays on the theory of numbers.
260			_aNew York _bDover Publications, Inc. _c1963
300			_a115 p. _ccm.
520			_aThis volume contains the two most important essays on the logical foundations of the number system by the famous German mathematician J. W. R. Dedekind. 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. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis. The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. 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.
650			_aMathematics- Irrational Numbers _9812934
700			_aWooster Woodruff Beman _eTranslator _9812935
942			_hB13 K3/SC _cREF _2CC _n0
999			_c623516 _d623516