Good Math: typo/Errata

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1

2022-09-10T00:00:00Z
Title: Good Math, by Mark C. Chu-Carroll, (page 20)
In chapter 3, Real Numbers, Part 2 Ordering, the 3rd axiom has an error. Note: I use “le” in place of “≤”, in case that latter symbol is not accepted on some parts of this website.
From the book:
3. If x le y. then for all z le 0, (x * z) le (y *z)
But example: if x = 3, y = 8, and z = -1,
then (3 * -1) le (8 * -1) = -3 le -8 is wrong!

Two suggestions for correction of this:
A) in “(x * z) le (y * z)”, replace le by ge (≥). However, ge (≥) has not been shown or defined so far in the book, so …
B) replace “(x * z) le (y * z)” by "(y * z) le (x*z), i.e. swap the two operands of the le operator.

Please also add the book’s tag if it has not already present, thanks! How do I do this? what does the tag look like? A: like this #book-good-math

2

Hello @jimf,

The author isn’t here on DevTalk but I will pass along your erratum. Thank you for reading and for pointing out the error!

Best wishes,
Margaret

3

Another report: Page 8, the last step of Peano Induction.

What’s there:

$\frac(n^2+3n+2}{2} = \frac{n^2+3n+2}{2}$

What should likely be the last step:

$\frac{n^2+3n+2}{2} = \frac{(n+1)(n+2)}{2} = \frac{(n+1)((n+1)+1)}{2}$

It’s all equal, but the last form is what I’d expect from a proof.

4

Thanks for the report @oddraisin. I’ll pass it along to the author.