=hbaker1@pop.pipeline.com I'm sure that you have read a lot more math papers than have I, but I can tell you that I have _never_ seen a math or computer science paper in which |N excluded 0. At least in the CS community, if you want the positives only, you need to say |N^+ (i.e., |N superscript +).
(Now I get to agree with Henry!<;-) Why the CS major flunked home economics: "Q: How many eggs in a dozen?" "A: Eleven: 0, 1, 2,...11!" Unfortunately, for math it's more of a mess. Per the MathWorldBook Weisstienlopedia, http://mathworld.wolfram.com/NaturalNumber.html "...The set of natural numbers is denoted N. Unfortunately, 0 is sometimes also included in the list of "natural" numbers (Bourbaki 1968, Halmos 1974), and there seems to be no general agreement about whether to include it. In fact, Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that [0 member P]." And then you're supposed to *avoid* confusion by using Z+ to mean N without 0, not to be confused with Z*, meaning N with 0...
=John Conway <conway@Math.Princeton.EDU> ...it doesn't work for general partial orders, for which "greater than or equals" doesn't mean the same as "not less than".
What we need is a single word (behaving like "over") for the simple concept ">=", which would allow "over-zero" to substitute for the present "non-negative".
Lest these points gets lost, the most serious lack is a good *generic* adjective, rather than just a symbol or noun denoting a particular set. I've recently struggled with simply describing pairs p in the domain Z* x Z* (aka NxN). Any p not (0,0) is "naturally" described as nonzero, but how the heck do you describe a general member of the domain (and, worse, include/exclude the boundary sets (0,n>0) and (n>0,0))? Yet I'm not too keen on "over-zero", since it suggests >0 not >=0. You don't say "overheated" to mean "not cold". John McCarthy's "from-zero" avoids this, but it doesn't sound grammatical, much less adjectival: "from-zero pair"? Maybe "upper" (as in "upper triangular", which *includes* the diagonal)?