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What is the difference between $Z_{+}$ and $Z_{++}$? Is the first all the non-negative integers and the second all the positive integers?

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Where did you find the latter notation? – anon May 23 '12 at 3:03
@anon: in a linear programming book. – robw May 23 '12 at 3:04
Can you give some context, e.g., tell us the sentence it appears in, and perhaps the sentence before and after it? (I would've said the difference is that the second one has a typographical error, but maybe that's not really correct. :)) – KCd May 23 '12 at 3:05
The meaning can vary by context. I've not seen the latter, but the former can mean the positive integers (or even the nonnegative integers), or even "the integers as a group under addition"). The book should explain the notation somewhere... – Arturo Magidin May 23 '12 at 3:06

Let's cover all the bases here:

It might be the case that you are right. In Foundations of Analysis in the Complex Plane (on this page in particular), or as seen below, it agrees with you. $Z^+$ is the set of nonnegative, $Z^{++}$ is the set of positive.

Image from book

But to be honest, I've never seen that notation before. Conceivably, Z++ is a reference to the object-oriented extension of Z Notation. I don't know much about this either, but it's briefed at wiki.

There is also a specific version of the C++ language that is denoted by Z++ (probably because it's more complicated).

I suppose the thing to take from this is that these symbols could refer to many things, but in particular they refer to whatever the author defined them to be. Hopefully, one of these makes more sense than the others.

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