‎RECHY John‎
‎NUMBERS‎

‎De la Controverse entre Mrs. Leibnitz & Bernouilli sur les Logarithmes des Nombres Negatifs e Imaginaires. (Controversy between Mr Leibniz and Mr Bernouilli on the logarithms of negative and imaginary numbers).‎

‎(Berlin, Haude et Spener, 1751). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome V, pp. 139-179.‎

‎First edition of this importent paper on the logarithms of complex numbers, where Euler clarified such functions. He disagreed with Leibniz that a special function was only applicable for positive numbers, and showed that i was applicable for both negative and positive numbers, only with a difference of a constant. When Euler here (the offered item) came out with the correct form for the logarithm, it was not generally accepted. - Enestrom, Euler Bibliography E 168.‎

‎Losev, A.F. The Dialectics of Numbers at the Plotin: (Translation and commentar‎

‎Losev, A.F. The Dialectics of Numbers at the Plotin: (Translation and commentary of Plotins treatise On Numbers) -/Losev, A.F. Dialektika chisla u Plotina: (Perevod i kommentariy traktata Plotina O chislakh)- Losev, A.F. The dialectics of numbers at the Plotin: (Translation and commentary of Plotins treatise On Numbers) -M: author, 1928.-194, 2. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUbd-2e41a30374605c4c.‎

‎Dedekind R. Continuity and Irrational Numbers. Proof of Transcendental Numbers ‎

‎Dedekind R. Continuity and Irrational Numbers. Proof of Transcendental Numbers In Russian /Dedekind R. Nepreryvnost i irratsionalnye chisla. Dokazatelstvo sushchestvovaniya transtsendentnykh chisel Peter from German S. Shatunovsky. Third edition Odessa Mathesis 1914. Translated with him S. Shatunovsky, private associate professor at Imperial Novorossiysk University. With the addition of an article by a translator: Proof of the existence of transcendental numbers 77g. We have thousands of titles and often several copies of each title may be available. Please feel free to contact us for a detailed description of the copies available. SKUalb3dac240e6ada396e.‎

‎Numbers, Measures, and the Transfer of Goods in Prehistory‎

‎, Brepols, 2024 Paperback, 122 pages, Size:216 x 280 mm, Illustrations:10 b/w, 25 col., 12 tables b/w., 1 maps b/w, 5 maps color, Language: English. ISBN 9782503610689.‎

‎Summary Numbers, weights, and measurements, and the systems underpinning them, have always been a fundamental part of human society. Developed in different ways and at different times, such systems have provided a foundation for science, technology, economics, and new ways of engaging with and understanding the world. This volume aims to explore the background to numbers and measurements in more detail by drawing together specialists from a growing field of research. The contributions gathered here offer new and interdisciplinary insights into how the development of mathematical ideas and systems evolved, early metrological systems, the exchange of goods and their impact, the standardization of measuring tools, and the impact of such concepts. This unique volume is deliberately set broad, both geographically and chronologically, in order to compare and contrast changes over time and between peoples, and in doing so it sheds new light on the social and scientific developments among both prehistoric and early historic societies. TABLE OF CONTENTS List of Illustrations Foreword 1. How to Open the Gift Box? Archaeology and the Transfer of Goods Christophe Darmangeat 2. Between East and West. The Measurement of Linearity as the Forerunner of Weighing Aleksander Dzby?ski 3. Feasting and Burial Rites in Pre-Hispanic Honduras. Comparing Archaeological and Ethnographic Evidence Franziska Fecher 4. Development and Functioning of Numeral Systems Jadranka Gvozdanovi? 5. Some Further Thoughts on Commodity and Gift Exchange in Tribal Societies Ju?rg Helbling 6. The Early Bronze Age Rib Ingot Hoard from Oberding (Upper Bavaria) Sabrina Kutscher 7. Numbers and Measures in the Iberian Peninsula during the Iron Age. Evidence from the Archaeological and Textual Records Thibaud Poigt and Coline Ruiz Darasse 8. Highly Composite Numbers and the Early Use of Weights Lorenz Rahmstorf 9. The Functions of Number in Early Greek Text Richard Seaford‎

‎[Church:] A note on the Entscheidungsproblem (+) Correction to A note on the Entscheidungsproblem (+) Review of ""A. M. Turing. On Computable numbers, with an application to the Entscheidungsproblem"" (+) [Post:] Finite combinatory processes-formulation... - [LANDMARK VOLUME IN THE HISTORY OF LOGIC]‎

‎[No place], The Association for Symbolic Logic, 1936 & 1937. Royal8vo. Bound in red half cloth with gilt lettering to spine. In ""Journal of Symbolic Logic"", Volume 1 & 2 bound together. Barcode label pasted on to back board. Small library stamp to lower part of 16 pages. A very fine copy. [Church:] Pp. 40-1" Pp. 101-2. [Post:] Pp. 103-5. [Turing:] Pp. 153-163" 164. [Entire volume: (4), 218, (2), IV, 188 pp.]‎

‎First edition of this collection of seminal papers within mathematical logic, all constituting some of the most important contributions mathematical logic and computional mathematics. A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) CORRECTION TO A NOTE ON THE ENTSCHEIDUNGSPROBLEM (+) REVIEW OF ""A. M. TURING. ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO THE ENTSCHEIDUNGSPROBLEM"":First publication of Church's seminal paper in which he proved the solution to David Hilbert's ""Entscheidungsproblem"" from 1928, namely that it is impossible to decide algorithmically whether statements within arithmetic are true or false. In showing that there is no general algorithm for determining whether or not a given statement is true or false, he not only solved Hilbert's ""Entscheidungsproblem"" but also laid the foundation for modern computer logic. This conclusion is now known as Church's Theorem or the Church-Turing Theorem (not to be mistaken with the Church-Turing Thesis). The present paper anticipates Turing's famous ""On Computable Numbers"" by a few months. ""Church's paper, submitted on April 15, 1936, was the first to contain a demonstration that David Hilbert's 'Entscheidungsproblem' - i.e., the question as to whether there exists in mathematics a definite method of guaranteeing the truth or falsity of any mathematical statement - was unsolvable. Church did so by devising the 'lambda-calculus', [...] Church had earlier shown the existence of an unsolvable problem of elementary number theory, but his 1936 paper was the first to put his findings into the exact form of an answer to Hilbert's 'Entscheidungsproblem'. Church's paper bears on the question of what is computable, a problem addressed more directly by Alan Turing in his paper 'On computable numbers' published a few months later. The notion of an 'effective' or 'mechanical' computation in logic and mathematics became known as the Church-Turing thesis."" (Hook & Norman: Origins of Cyberspace, 250) Church coined in his review of Turing's paper the phrase 'Turing machine'.FINITE COMBINATORY PROCESSES-FORMULATION I: The Polish-American mathematician Emil Post made notable contributions to the theory of recursive functions. In the 1930s, independently of Turing, Post came up with the concept of a logic automaton similar to a Turing machine, which he described in the present paper (received on October 7, 1936). Post's paper was intended to fill a conceptual gap in Alonzo Church's paper on 'An unsolvable problem of elementary number theory'. Church had answered in the negative Hilbert's 'Entscheidungsproblem' but failed to provide the assertion that any such definitive method could be expressed as a formula in Church's lambda-calculus. Post proposed that a definite method would be one written in the form of instructions to mind-less worker operating on an infinite line of 'boxes' (equivalent to the Turing machines 'tape'). The range of instructions proposed by Post corresponds exactly to those performed by a Turing machine, and Church, who edited the Journal of Symbolic Logic, felt it necessary to insert an editorial note referring to Turing's ""shortly forthcoming"" paper on computable numbers, and asserting that ""the present article ... although bearing a later date, was written entirely independently of Turing's"". (Hook & Norman: Origins of Cyberspace, 356).COMPUTABILITY AND LAMBDA-DEFINABILITY (+) THE Ø-FUNCTION IN LAMBDA-K-CONVERSION: The volume also contains Turing's influential ""Computability and lambda-definability"" in which he proved that computable functions ""are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene"". (Hook & Norman: Origins of Cyberspace, 395).‎