?? you can substitute equal functions for functions and equal values for values, but the trouble starts when you try to substitute one function for another just because they have equal vlaues at one point ... ??? .... ?? "evaluation at x" as operator vs as conceptual blurring / mistake .... ??? .....

?? "graph" over time of "president of usa" vs of "barack obama", for example ... ?? photographs .... ???? ...

zeno's (non-)moving arrow paradox ...

referential opacity paradox ...

f'(x) = 0 mistake .... ??? .....

?? chain rule ... ???? ....