Good point! I’m not a mathematician so the pedagogy here doesn’t really irk me. But, I do also believe that teachers should be held to a higher standard, especially when writing out educational text. Thanks for the clarification!

Also, I bet the authors weren’t intentionally trying to lead readers astray with that statement. Most books have a preface with some point of contact if you find errors. I’m sure if you wrote in the authors would be happy to fix this up :)

I wouldn't say it's a nitpick. Rationals are fractions of integers, not just any fractions at all. Rationals are _examples_ of reals, but it's bad pedagogy to say "fractions, which are called reals" because it sounds like the authors are giving a definition of reals. While they technically did not say this was a definition, it is sloppy.

Fractions = rational numbers, which are an infinitely small subset of the real numbers. The rest of the reals are irrational numbers, of which pi and e are examples.