I have a function f: R -> R such that f(0)=1 and f'(x)=f(x). Is this concealing a parameter? It turns out we can deduce that f(x)=e^x, so f(x)=pow(e,x), so mayb

I have a function f: R -> R such that f(0)=1 and f'(x)=f(x). Is this concealing a parameter? It turns out we can deduce that f(x)=e^x, so f(x)=pow(e,x), so maybe? But wait, is pow concealing another parameter? Indeed, exponentiation is just (a completion over) repeated multiplication; multiplication is repeated addition, and addition repeated succesorship. It's straightforward to show that pow(x,y)=f(2,x,y) where f(n,x,y) encodes said hierarchy. But wait! f is a function, which is a set of 2-tuples, so we have another "hidden" parameter. It's also essentially part of Fast growing hierarchy[0] functions. Or what if we extend to complex numbers? Is the imaginary axis degree of freedom another hidden parameter? Et cetera ad infinitum... So, if you want to say that sqrt(x) has a hidden parameter, you're just making an arbitrary claim unless you accept it is concealing an unbounded number of hidden parameters. Or we can just do the obvious thing and say that sqrt(x) has one parameter. [0]:https://googology.fandom.com/wiki/Fast-growing_hierarchy https://googology.fandom.com/wiki/Fast-growing_hierarchy