

Texas high school math text claims no bijection between integers and rationals - DavidSJ
https://www.reddit.com/r/math/comments/3k1qe6/this_is_in_a_high_school_math_textbook_in_texas/

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hugh4
It's obviously just one guy's screwup, but it got me thinking.

For first-year university subjects, there's a smallish number of textbooks
across the globe. For first-year physics, you're using Halliday and Resnick,
or ... a half-dozen or so others whose names escape me right now. But the
point is that a small number of decent textbooks exist, and they tailor the
courses to the textbooks.

The existence of a "Texas high school math text" makes me think that at the
K-12 level, textbooks are tailored to the courses instead of vice versa. So
you've got second-rate authors writing textbooks just for one market
(admittedly Texas public schools is a big market that most authors would be
very happy to have a monopoly over) and it makes it more likely that errors
like this will slip through.

Calculus is the same the world over, it doesn't make sense for Texas to have a
different textbook to Toronto or Toowoomba.

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ColinWright
There's even an explicit bijection that has a formula associated with it:

[https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree](https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree)

