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Isn’t this technically true though? Fractions are just rational reals. The examples listed are still reals, just irrational.
by _gabe_ 3y ago
Isn’t this technically true though? Fractions are just rational reals. The examples listed are still reals, just irrational.
- vcxy 3y agoIt's bad pedagogy. But it is also technically incorrect. You can have fractions with complex numbers.
- _gabe_ 3y agoGood 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 :)
- gcr 3y agoi think i can see the nitpick here: pi and e aren't representable as rational numbers, and aren't representable exactly in IEEE754
- vcxy 3y agoI 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.
- Keysh 3y agoFractions = 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.
- whatisyour 3y agoFraction doesn't have to be rational.