On the meaning of $\mathbb{R_+}$

Question

$\mathbb{R_+}=[0,+\infty]$ or $\mathbb{R_+}=[0,+\infty)$?

Thanks!

Answer 1

Since $\infty$ is not a real number, $\Bbb R_+=\{x\in\Bbb R\mid x>0\}=(0,{+}\infty)$.

In some places, however, $0$ might be included (if my memory serves me right the French system is to include $0$ in the term "positive"), in which case this is $[0,{+}\infty)$.

Answer 2

If not specified $\mathbb{R_+}$ means $(0, \infty)$. We generally don't include $\infty$ in this case and also $0$.