The theory of sets, described in the preface to this book as 'Georg Cantor's magnificent theory' was first developed in the 1870s, and was recognised as one of the most important new branches of mathematical science. W. H. Young and his wife Grace Chisholm Young wrote this book, published in 1906, as a 'simple presentation'; but they warn that it is effectively a work in progress: the writing '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 Young's were a dynamic force in mathematical research: William had been Grace's tutor at Girton College; she was subsequently the first woman to be awarded a Ph. D by the University of Goettingen. Cantor himself said of the book: 'It is a pleasure for me to see with what diligence, skill and success you have worked.'
The theory of sets, described in the preface to this book as 'Georg Cantor's magnificent theory' was first developed in the 1870s, and was recognised as one of the most important new branches of mathematical science. W. H. Young and his wife Grace Chisholm Young wrote this book, published in 1906, as a 'simple presentation'; but they warn that it is effectively a work in progress: the writing '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 Young's were a dynamic force in mathematical research: William had been Grace's tutor at Girton College; she was subsequently the first woman to be awarded a Ph. D by the University of Goettingen. Cantor himself said of the book: 'It is a pleasure for me to see with what diligence, skill and success you have worked.'
Preface; 1. Rational and irrational numbers; 2. Representation of numbers on the straight line; 3. The descriptive theory of linear sets of points; 4. Potency, and the generalised idea of a cardinal number; 5. Content; 6. Order; 7. Cantor's numbers; 8. Preliminary notions of plane sets; 9. Regions and sets of regions; 10. Curves; 11. Potency of plane sets; 12. Plane content and area; 13. Length and linear content; Appendix; Bibliography; Indexes.
An introduction from 1906 to a then new and continuously developing branch of mathematical science.
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