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