4 ms·

Eh, I think it's fair to consider the natural numbers as either the non-negative, nonzero integers or the non-negative integers. As long as an author declared w

Eh, I think it's fair to consider the natural numbers as either the non-negative, nonzero integers or the non-negative integers. As long as an author declared which use they intend front and center, I don't think one or the other is more "right." Very established texts and papers alternate freely between including and not including 0.

jessaustin 8y ago
As the author says, it's a matter of taste. The author's good taste is "right" in the same sense that e.g. 0-indexed arrays are "right": it avoids problems that not including zero causes. How many elements are in the empty set? Why shouldn't the natural numbers be able to answer that question?
- hopler 8y ago
  What is 0 minus 1? Why isn't that a natural number? Why shouldn't the nth natural number be N? The author's own book discusses the 1st prime, in chapter 0, which begins on page 1. How is this natural? Problem 0.4 Add the odd numbers between 1 and 30." Why would you say 1 and 30 instead of 0 and 30, since 0 is natural? Getting hung up on notation and arguing over conventions will hold you back from learning math. Offsets (0) and ordinals (1) aree both useful in arrays. The only thing wrong* is not saying which you mean. http://exple.tive.org/blarg/2013/10/22/citation-needed/ http://exple.tive.org/blarg/2013/10/22/citation-needed/
- throwawaymath 8y ago
  You shouldn't consider offsets ("0-indexed") more valid or right than ordinals ("1-indexed"). Doing so imposes unnecessary restrictions and narrows your scope of discussion to the programming context instead of broader mathematics. You can come up with any arbitrary case where it alternatively makes sense or doesn't make sense to include 0 in the natural numbers. If something is a matter of taste, it really doesn't make sense to say one taste is "right" over another. It's more important to define your terms and be consistent for the context you're working in.

jessaustin 8y ago

As the author says, it's a matter of taste. The author's good taste is "right" in the same sense that e.g. 0-indexed arrays are "right": it avoids problems that not including zero causes. How many elements are in the empty set? Why shouldn't the natural numbers be able to answer that question?

hopler 8y ago
What is 0 minus 1? Why isn't that a natural number? Why shouldn't the nth natural number be N? The author's own book discusses the 1st prime, in chapter 0, which begins on page 1. How is this natural? Problem 0.4 Add the odd numbers between 1 and 30." Why would you say 1 and 30 instead of 0 and 30, since 0 is natural? Getting hung up on notation and arguing over conventions will hold you back from learning math. Offsets (0) and ordinals (1) aree both useful in arrays. The only thing wrong* is not saying which you mean. http://exple.tive.org/blarg/2013/10/22/citation-needed/ http://exple.tive.org/blarg/2013/10/22/citation-needed/
throwawaymath 8y ago
You shouldn't consider offsets ("0-indexed") more valid or right than ordinals ("1-indexed"). Doing so imposes unnecessary restrictions and narrows your scope of discussion to the programming context instead of broader mathematics. You can come up with any arbitrary case where it alternatively makes sense or doesn't make sense to include 0 in the natural numbers. If something is a matter of taste, it really doesn't make sense to say one taste is "right" over another. It's more important to define your terms and be consistent for the context you're working in.