This textbook uses 0-based indexing which is extremely silly because everything would be a lot clearer in 1-based indexing, there's literally no reason to use 0-based (which come from array indexing origins), and it leads to typos like this one
Abstruse friend@nonphatic It also comes from the fact that 0 is a natural number, so all (non-empty) initial sequences of naturals will contain it.
hannah 
[:aqua_trauma_1::aqua_trauma_2::aqua_trauma_3::cockwalk.gif:]@abs @nonphatic sorry for off-topic but don’t say that too loud at school or you will ignite a debate 
Starbright Electric Bolt@nonphatic This is all subjective, but zero indexing is just overall better I think? It's true that you can get in trouble the way the authors have, but I'd blame that on the "a,...,b" notation. With indexes the way you suggest, the sentence at the end would have to end "iff for all 0 < i <= k:". And it's true that it's less clear if you aren't used to it, but I think it's just like switching to the metric system or etc.
@starbright I'd just shift the bounds of the inequality, then you'd say 1 <= i <= k
Personally I think inclusive ranges are easier to think about, but yeah this is just a matter of being used to it
But! My gripe is that a) there's k-1 everywhere that's extra clutter compared to just using k, and b) the projection functions range from P^n_0 to P^n_{n-1}, and it really really irks me that the superscript and subscript don't match at that last one
Personally I think inclusive ranges are easier to think about, but yeah this is just a matter of being used to it
But! My gripe is that a) there's k-1 everywhere that's extra clutter compared to just using k, and b) the projection functions range from P^n_0 to P^n_{n-1}, and it really really irks me that the superscript and subscript don't match at that last one
@starbright and the sequencing notation a_0, ..., a_{k-1} is used a LOT in this book and it would be a whole lot easier to read it like "from the first element a_1 to the kth element a_k"