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Author: Fred Katz
Publisher:
ISBN: 9781544217604
Category :
Languages : en
Pages : 120
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Book Description
Cantor's theory of cardinality violates common sense. It says, for example, thatall infinite sets of integers are the same size. This thesis criticizes the argumentsfor Cantor's theory and presents an alternative.The alternative is based on a general theory, CS (for Class Size). CSconsists of all sentences in the �rst order language with a subset predicate and aless-than predicate which are true in all interpretations of that language whosedomain is a �nite power set. Thus, CS says that less than is a linear orderingwith highest and lowest members and that every set is larger than any of itsproper subsets. Because the language of CS is so restricted, CS will have infiniteinterpretations. In particular, the notion of one-one correspondence cannotbe expressed in this language, so Cantor's definition of similarity will not be inCS, even though it is true for all finite sets.
Author: Fred Katz
Publisher:
ISBN: 9781544217604
Category :
Languages : en
Pages : 120
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Book Description
Cantor's theory of cardinality violates common sense. It says, for example, thatall infinite sets of integers are the same size. This thesis criticizes the argumentsfor Cantor's theory and presents an alternative.The alternative is based on a general theory, CS (for Class Size). CSconsists of all sentences in the �rst order language with a subset predicate and aless-than predicate which are true in all interpretations of that language whosedomain is a �nite power set. Thus, CS says that less than is a linear orderingwith highest and lowest members and that every set is larger than any of itsproper subsets. Because the language of CS is so restricted, CS will have infiniteinterpretations. In particular, the notion of one-one correspondence cannotbe expressed in this language, so Cantor's definition of similarity will not be inCS, even though it is true for all finite sets.
Author: Michael Hallett
Publisher: Oxford University Press
ISBN: 9780198532835
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author: Fredric M. Katz
Publisher:
ISBN:
Category : Cardinal numbers
Languages : en
Pages : 410
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Book Description
Author: William Stuart
Publisher:
ISBN:
Category : Potatoes
Languages : en
Pages : 44
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Book Description
Pp. 35.
Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486795497
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.
Author: Vladimir Kanovei
Publisher: Springer Science & Business Media
ISBN: 366208998X
Category : Mathematics
Languages : en
Pages : 421
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Book Description
In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.
Author: Robert S. Webb
Publisher:
ISBN:
Category : Particle size determination
Languages : en
Pages : 44
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Book Description
Author:
Publisher:
ISBN:
Category : Marine engineering
Languages : en
Pages : 608
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 48
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Book Description
Author: Jeremy Ramsden
Publisher: Springer
ISBN: 1447167023
Category : Computers
Languages : en
Pages : 313
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Book Description
This comprehensive textbook presents a self-contained guide to bioinformatics, defined in its broadest sense as the application of information science to biology. Thoroughly updated and greatly expanded, this third edition now includes material on the growing array of “-omics”; covering metagenomics, toxicogenomics, glycomics, lipidomics, microbiomics and phenomics. New chapters have also been added on ecosystems management and the nervous system. Emphasis is placed on providing both a firm grounding in the core concepts and a clear overview of the complete field of bioinformatics. Features: explains the fundamentals of information science relevant to biology; covers both organismal (ontogeny and phylogeny, as well as genome structure) and molecular aspects; examines the most important practical applications of bioinformatics, providing detailed descriptions of both the experimental process and the data analysis; provides a varied selection of problems throughout the book, to stimulate further thinking.
