If negative numbers are legitimate, then the rules of arithmetic must be extended to include them. Here is a puzzling peculiarity related to Arnauld's concern about ratios: Multiplication is an extension of the idea of repeated addition. For any numbers a and b, a < b implies (-5) + a < (-5) + b but (-5) a > (-5) b. How do you resolve this apparent inconsistency?
If negative numbers are legitimate, then the rules of arithmetic must be extended to include them. Here is a puzzling peculiarity related to Arnauld's concern about ratios: Multiplication is an extension of the idea of repeated addition. For any numbers a and b, a < b implies (-5) + a < (-5) + b but (-5) a > (-5) b. How do you resolve this apparent inconsistency?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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If negative numbers are legitimate, then the rules of arithmetic must be extended to include them. Here is a puzzling peculiarity related to Arnauld's concern about ratios:
- Multiplication is an extension of the idea of repeated addition.
- For any numbers a and b, a < b implies (-5) + a < (-5) + b but (-5) a > (-5) b.
How do you resolve this apparent inconsistency?
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