elementary set theory - Bijection between $mathbb N^+ times mathbb R^+$ and $mathbb R^+$

Let $\mathbb N^+$ denote the set of natural numbers bigger than $0$ and let $\mathbb R^+$ denote the set of real numbers bigger than $0$.

Is there a way to write down an explicit bijection between $\mathbb N^+ \times \mathbb R^+$ and $\mathbb R^+$?

Answer

You can replace $\mathbb{N}^+$ by $\mathbb{N} = \{ 0 , 1 , 2 ... \}$. Also $\psi : \mathbb{R}^+ \cong [0,1)$.
Then the required bijection can be

$$\mathbb{N} \times \mathbb{R}^+ \ni (n,r) \longmapsto n+\psi(r) \in \mathbb{R}^+ \ .$$