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On Some Difficulties in the Theory of Transfinite Numbers and Order Types
Author(s) -
Russell B.
Publication year - 1907
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s2-4.1.29
Subject(s) - transfinite number , order (exchange) , citation , computer science , mathematics , type (biology) , discrete mathematics , library science , ecology , finance , economics , biology
DR. HOBSON'S most interesting paper in the Proceedings of the London Mathematical Society* raises a number of questions which must be answered before the principles of mathematics can be considered to be at all adequately understood. I do not profess to know the complete answers to these questions, and most of the present paper will consist only of tentative suggestions, made as possibly a step towards the true solutions, not as themselves constituting solutions. With the greater part of Dr. Hobson's paper I find myself in agreement ; my purpose, therefore, will not be in the main polemical, but rather to carry the discussion a stage further by introducing certain distinctions which I believe to be relevant and important, and by generalizing as far as possible the difficulties and contradictions hitherto discovered in the theory of the transfinite. There are two wholly distinct difficulties to be considered in the theory of transfinite cardinal numbers, namely :