TITLE: What is the meaning of $\mathbb R^+$?
QUESTION [7 upvotes]: For a function $f$ that maps set $A$ to $B$,

$f\colon\mathbb R^+\to\mathbb R^+$, $f(x) = x^2$ is injective.
$f\colon\mathbb R\to\mathbb R$, $f(x) = x^2$ is not injective since $(- x)^2 = x^2$.

what is the difference between $\mathbb R^+$ and $\mathbb R$?
Additionally, what is the difference between $\mathbb N$ and $\mathbb N^+$?

REPLY [6 votes]: Simply $\mathbb R$ means the set of real numbers.
$\mathbb R^+$ means the set of positive real numbers.
And $\mathbb R^-$ means the set of negative real numbers.