I need to find two functions, if exist. The first is a function from $\mathbb{R}^2$ to $\mathbb{R}$ which is onto but not one to one. The second if a function to $\mathbb{Z}$ to $\mathbb{R}$ which is both one to one and onto $\mathbb{R}$.
I think I solved the first one: $f(x,y)=x$ if $x\ge y$, or $f(x,y)=y$ if $x<y$.
I can't find the second one does it exist ? Thank you !
I simpler solution for the first problem would be $f(x,y)=x$. There is no function from $\mathbb Z$ onto $\mathbb R$, since $\mathbb Z$ is countable, whereas $\mathbb R$ is uncountable.