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Paperback. Cover and spine in good condition. Spine is tight. Pages are clean, no markings, notes or stains. Ships from Friends bookstore to benefit Beaverton (Oregon) library.

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another.Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated.Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.

GIAM (a Gentle Introduction to the Art of Mathematics) is a free, open-source textbook -- the current version is 3.1. GIAM covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof (direct, indirect, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic).

The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large.

This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another.Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated.Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the same author, the present work is much larger than either of these. It contains solutions to many of the open problems of the earlier volumes. Among the new topics are continuum cardinals on Boolean algebras, with a lengthy treatment of the reaping number. Diagrams at the end of the book summarize the relationships between the functions for many important classes of Boolean algebras, including interval algebras, tree algebras and superatomic algebras.

This beautifully simple wooden log has equal-sized holes which will encourage children to count out the correct number of sticks from a pile, and then count in the correct number for each section. When placed correctly in the sections, children can easily see the difference between the numbers (cardinality). Each side of the log shows a different range of numerals (1-10 on one side and 0-9 on the other) making it helpful to teach number order and the value of zero. Made from FSC (Forest Stewardship Council) certified beechwood, the log measures 18-1/2 inches and includes 60 sticks measuring 2-1/2 inches. Safe for age 18m+. AN EARLY MATH MANIPULATIVE: Young minds will love this hands-on teaching aid in learning how to count, add and subtract.; MOTIVATE AND STIMULATE: Great STEM educational math manipulatives for preschoolers.; HOW TO PLAY: Place the number of sticks in the corresponding numeric slot and teach number recognition and counting. When placed correctly in the sections, children can easily see the difference between the numbers.; GROW YOUNG MINDS: Explore counting and cardinality for ages 18 months and up.; INCLUDES: One log that measures 18-1/2 inches and 60 sticks measure 2-1/2 inches.; count counting math mathematics addition number recognition numerals STEM Educational toys math manipulatives natural toys wooden toys Montessori count counting math mathematics addition number recognition numerals STEM Educational toys math manipulatives natural toys wooden toys Montessori