What does $\mathbb Z_+$ mean?

Question

I am not so sure whether the meaning of $$\mathbb Z_+$$ is very clear. How many different definitions are there? Does the definition that is used depend on whether the writer is English or German?

In French maths, this notation doesn't exist.

Answer 1

Many people would interpret this to mean $\{1,2,3,\ldots\}$, although some might argue for $\{0,1,2,3,\ldots\}$. Absent any other context I don't think any other interpretations are likely.

Sadly, many authors use notations without defining them, because they are "standard" in their little corner of mathematics.

Answer 2

Symbol "$+$" means "positive", so $\mathbb{Z}_+$ shoud properly be understood as $\{1,2,3,\ldots\}$. It's less confusing that undefined $\mathbb{N}$ in some paper, where we don't know if it includes $0$.

Answer 3

For the French notation $\mathbb N=\{0,1,2,3,\ldots\}$ and $\mathbb N^*=\{1,2,3,\ldots\}$ and and the notation $\mathbb Z_+$ is not used in general but it means $\mathbb N$.