User:Dominus/Ordinals


 * Computer programmers and other people who often deal with 0-indexed sequences run into this problem a lot, because conventional terms are designed for use with 1-indexed sequences, and switch from one linguistic form to another between "second" and "third". "First" does not contain any reference to the number 1 in the way that "fourth" refers to the number 4. Rather, "first" means initial or principal, not "in position #1".  So it is a solecism to use "first" for an item in the #1 spot if there is a preceding #0 item.  This is why it is a joke to say that you are first in line for the throne of England because Prince Charles is -3,945,286th in line.  Similarly there is nothing in the word "second" that suggests the number 2. Numbers don't appear in the names of ordinals until the third, which really does mean "in the #3 position".


 * So there is a conflict between the meaning of "first" and "second" and the meaning of "third", "fourth", etc. except in the case of 0-based sequences.


 * There are two not-obviously-crazy ways to resolve this.


 * You can say that element #0 is "zeroth", element #1 is "first", element #2 is "second", element #3 is "third". This abandons the traditional and conventional meaning of "first", so my preference is strongly for the other, which is to say that element #0 is "first", element #1"is "second", element #2 is "third", element #3 is "fourth", and so on.


 * The ambiguity in this case is not in the phrase "the first 5", but in whether the Fibonacci sequence starts with 0,1,1,2,3 or with 1,1,2,3,5. That has been