Sets and Their Sizes

Download or read book Sets and Their Sizes written by Fred Katz and published by . This book was released on 2017-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.