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 $\mathbb N^+$?