4 ms·

And yet, the set of natural numbers in mathematics is most often taken to start at 1. Mathematicians don’t have a problem with indexing.

• mcguire 6y ago
  Is it? Most nat's are built from zero and succ(n) in my experience.
  • vcxy 6y ago
    (I'm a mathematician) Honestly, not that many people in math think about the construction of the natural numbers frequently. Yeah, we learn about it of course, but that's about it. Very often the natural numbers do not include 0. Often they do. I've seen $\mathbb Z_{\geq0}$ and $\mathbb Z_+$ used to avoid having to worry about it. Hell, different countries can't even agree on whether 0 is positive. In France, 0 is considered both positive and negative. In USA, 0 is considered neither. (quick edit: I realize my last paragraph makes the $\mathbb Z_+$ option seem weird. I do math in the States.)
    • mcguire 6y ago
      That's what Wolfram Mathworld suggests: specifying a subset of the integers. :-)
  • lupire 6y ago
    Only if you need zero, which you don't need for indexing. Peano's original axioms started from 1 (which is logically equivalent to starting from 0, or -1, or potato) if all you are doing is counting)
• randomswede 6y ago
  In Sweden, the set usually referred to as "de naturliga talen" (the natural numbers) is any number n such that 0 <= n. Or, at least, that was the case when I did maths there. No idea what the default interpretation is these days. This is mostly why I don't say "natural numbers" and instead say "positive integers" or "non-negative integers", depending on if I want 0 included or not.