I have been thinking about the possibility of representing all points in a $4$-dimensional spacetime coordinate system $\mathbb{R}^{1,4}$, as points on one line $P$ (or axis of a $1$-dimensional coordinate system $\mathbb{R}^1$).
Then if $X$ is a point on $P$, and ($ct,x,y,z$) is the corresponding point in $\mathbb{R}^{1,4}$, we must have $X=f(ct,x,y,z)$, where the values of the function $f$ must be different for all values of the $ct,x,y$ and $z$.
For example, function $f(ct,x,y,z)=ct+x+y+z$, is not possible, because, for two different inputs of ($ct,x,y,z$), one can have the same result for $f$. Similarly, $f(ct,x,y,z)=ctxyz$ also cannot work.
Is there any function $f$ that can satisfy the above mentioned required property?
Edit: I'm looking for a bijective function $f$ that takes 4 inputs and gives a unique value for each input set.
