Define a bijection from $(0,1]$ to $[0, \infty)^2$
Route to follow,
A-) First define a bijection from $(0,1]$ to $(0,1]^2$
B-) Since there is a bijection from $(0,1]$ to $[0, \infty)$, namely $f(x) = (1/x) -1$, there is a bijection from $(0,1]^2$ to $[0, \infty)^2$
B says, if $f:A \rightarrow B$ is a bijection then there is a bijection $h:A^2 \rightarrow B^2$
Can anyone define me a function that satisfies A, and a function h for proof of B.
Rigor at elementary - intermediate analysis level will be appericiated.
Note: If possible I wonder the validity of infinite decimal approach for defining a function for part A.