The Theory Of Sets Of Points Classic Reprint

Excerpt from The Theory of Sets of Points The difficulties in arrangement which this fact, suggests have been enhanced by the nature of the subject itself and by the tentative character of some of its results. The writing of the book has necessarily involved attempts to extend the frontier of existing knowledge, and to fill in gaps which broke the connexion between isolated parts of the subject. The' references in the text which do not give the name of the author always refer to my own papers; in this connexion, however, I should like to out that the citations in the text are not to be regarded any means complete, and are supplemented by the list of literature at the end of the volume. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

Excerpt from On Some Antiquities in the Neighbourhood of Dunecht House Aberdeenshire It was known to the archaeologist that there were ogam inscriptions in the district, two Of them being among the most important in Caledonia; and that within an easy motor drive there was a minuscule inscription of six lines Of which no satisfactory explanation had been given. This inscription they had visited in a previous year. Further, the quick eye Of the hostess of Dunecht had caught sight of some curious sculptures on a stone by the road-side on the way to the minus cule inscription; and other like stones in the neighbourhood had been shewn in Stuart's two volumes of Sculptural Stones of Scotland. The suggestion was then made that for the sake of visitors at Dunecht a sort Of guide book should be prepared, giving some simple description of the several Objects and their meaning and uses. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from The Correspondence of Henrik Ibsen ON the 3lst of May 1880, Henrik Ibsen wrote to his publisher, Frederik Hegel, that he had begun a little book in which he intended to give some account of the outward and inward conditions under which each one of his works had come into being (letter It was to be called From Simian, to Rome, and was to give descriptions of his life at Skien and Grimstad, Bergen and Christiania, Dresden, Munich, and Rome. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from The Edinburgh New Philosophical Journal, 1828 A few Remarks on the class Mollusca in Dr fleming's Work on British Animals; with Descriptions of some new Species. By george johnston, M.D. Fellow of the Royal College of Surgeons of Edinburgh. Communicated by the Author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Evolution and the Need of Atonement As the title indicates, the main object of this book is not to offer a new theory of the Atonement. Rather it is intended to Show that when the origin and history of man are studied from the scientific, and especially the biological side, the spiritual life, its partial failure, and the need for Atonement, far from receding into vagueness and unreality, are thrown into strong relief. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Excerpt from Observations Upon the Natural History of Epidemic Diarrhoea The causative agencies from which springs the plentiful harvest of child mortality in large cities may be conceived as a felted mass of rootlets almost inextricably intertwined. Those of poverty, bad housing, bad feeding, and neglect, may be severally recognized, but the extent of their interrelations with actual respiratory and alimentary disease - those to which the greater part of the mortality is referred - can be traced only with difficulty. It is the object Of this work to aid ln the labour of cutting away the matrix and entangling fibres and to lay bare the hidden ramifications of at least one important causative agency - epidemic diarrhoea. This affection - if we accept provisionally the more novel and generally favoured conception. As to its nature - is revealed as something very like an ordinary infectious disease, and one which permeates all classes, while the excessive mortality it gathers round itself in urban centres must be regarded as something superadded, owing to the vicious circle it forms with those baneful conditions of slum life mentioned above. On the other hand, its peculiarly intimate association with the circum stances of domestic life, from the continual faecal pollution of the interior of the household by infants and others, tends to make it more so than other affections of the kind peculiarly a class disease, and an especial scourge of dirty neighbourhoods. Dirty towns may however be saved from excessive mortality by a high percentage of breast feeding. A notable point in the interesting comparison that can be drawn between diarrhoea and typhoid fever is that, in accordance with their peculiarly opposite age-incidence curves, the marked and habitual depositing of infectious excreta within the household in the former disease may make the question of water-closet versus conservancy pan a matter of far less importance than in the latter. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.