4 ms·

In reply to a dead comment: The most common definition of natural numbers is "positive integers." I do agree that 0 is important enough that it would have merit

• ot 12y ago
  It is somewhat controversial: according to Wikipedia There is no universal agreement about whether to include zero in the set of natural numbers. Today some textbooks, especially college textbooks, define the natural numbers to be the positive integers {1, 2, 3, ...}, while others, especially primary and secondary textbooks, define the term as the non-negative integers {0, 1, 2, 3, ...}. Among mathematicians, the most common (by far) definition is the one given by Peano axioms, which include 0. Including 0 is very convenient for a number (pun intended) of reasons, for example it makes the naturals a monoid, and it is easier to define the integers.
  • ska 12y ago
    Pedantic: they are still a commutative monoid without 0, under multiplication with identity 1. You need 0 as the identity for addition, which is fundamental in these constructions.
  • OscarCunningham 12y ago
    I'm not sure if it is more common to say that 0 is a natural number. There's a math.stackexchange thread about this which seems to have equally many people saying that each is the more common one. http://math.stackexchange.com/questions/283/is-0-a-natural-number http://math.stackexchange.com/questions/283/is-0-a-natural-n... (I count 4 people saying {1,2,3,...} is more common vs 3 saying {0,1,2,...} is more common. I also notice that N_0 is used by both sides to refer "unambiguously" to the convention of the other side.) In my experience {1,2,3,...} is used more in number theory, and {0,1,2,...} is used more in logic.