4 ms·
Texas high school math text claims no bijection between integers and rationals
- hugh4 11y agoIt'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.
- ColinWright 11y agoThere'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