Is there some polynomial, for example, $f(x)=x^2-3x+2$, such that when you plug in$f(1), f(2), f(3),$ etc, when the output is considered as a string of characters, no output is within another? Clearly no input can be equal to another. For example, the polynomial above doesn't work because $f(1)=f(2)$, and $f(5)=12,$ and $f(3)=2$. The output of 5 contains the output of 3.
Suppose that some output was $65$, and another was $129878565980$. There would be a violation because $1298785 \mathbf {65}980$ contains $65$. Sorry if this is unclear, I was not sure how to explain it.