arithmetic without introducing inconsistencies. Explain the reasoning leading to Wallis's paradoxical claim that, if negative numbers are less than zero, they must be greater than infinity. Wallis's argument depends, in part, on the assertion that (3/-1) = -3. Must this be true? Why or why not? If a student proposed Wallis's argument, how would you respond?

arithmetic without introducing inconsistencies. Explain the reasoning leading to Wallis's paradoxical claim that, if negative numbers are less than zero, they must be greater than infinity. Wallis's argument depends, in part, on the assertion that (3/-1) = -3. Must this be true? Why or why not? If a student proposed Wallis's argument, how would you respond?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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John Wallis and other 17th century mathematicians were struggling with how to fit negative numbers into arithmetic without introducing inconsistencies.

Explain the reasoning leading to Wallis's paradoxical claim that, if negative numbers are less than zero, they must be greater than infinity.
Wallis's argument depends, in part, on the assertion that (3/-1) = -3. Must this be true? Why or why not?
If a student proposed Wallis's argument, how would you respond?

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