On the Foundation and Technic of Arithmetic (Classic Reprint) - Softcover

Halsted, George Bruce

Softcover

ISBN 10: 1440082812 ISBN 13: 9781440082818

Publisher: Forgotten Books, 2010

Synopsis

In the French Revolution, when called before the tribunal and asked what useful thing he could do to deserve life, Lagrange answered: "I will teach arithmetic." Almost invariably now arithmetic is taught by those whose knowledge of mathematics is most meager. No wonder it and the children suffer. In this day of the arithmetization of mathematics and later its logicization, are the beauty, the elegance of arithmetical procedures to remain still unexplained? Is the singular, the lonely precision of this science and art to remain unheralded, unexpounded? In arithmetic a child may taste the joy of the genius, the joy of creative activity. Arithmetic is for man an integrant part of his world construction. Thus do his fellows make their world, and so must he. Now this is not by passive apprehension of something presenting itself, but by permeating vitalization spreading life and its substance through what the ignorant teacher would present as the dead mechanism of mechan

Table of Contents

CHAPTER PAGB; Introduction , 1; 1 The Prehuman Contributions to Arithmetic 3; The natural individual, J-The artificial individual, 4--Primary; Dumber, 5·-0ur base ten, 7; II The Genesis of Number; III Counting and Numerals; Correlation, 10-To count II-The primitive standard sets, JJ; -The abacus, 12-The word'Il1meral system, 12-Periodicity, IJ; -A partitioned unit, 14-Number without counting, 14-Decimal; word-numerals, 14-Invariance of cardinal, IS; 8; 10; IV Genesis of our Kumbcr Notation 17; Positional counting 17-The abacus, li'-Recorded symbols, 18; -The Hindu numerals ] g-The zerO 20-0ur present notation,; 22; V The Two Direct Operations, Addition and Multiplication 26; Notation, 26-The symbol =, 26-Inequality, 27-Parentheses; 28-Expressions 28-Substitution, 29-Addition, 29-Formulas,; 32-ordinal addition, 33-Properties of addition 33-Multiplication,; 35; VI The Two Inverse Operations, Subtraction and Division 39; Inversion, 3

Edition details

• Publisher: Forgotten Books
• Publication date: 2010
• Language: English
• ISBN 10: 1440082812
• ISBN 13: 9781440082818
• Binding: Paperback
• Number of pages: 148