To the last question i know the answer immedeately. Some irrationals are no root of any FINITE polynomial, actually there are more numbers wich aren't
-IF such a function exists it has to be a polynomial to get rational output with rational input.
I change this to something that excludes nasty functions like exponentials and logarithms and such
"Expressable by a polynomial or a quotient of two polinomials, and the quotient/sum of things made in that fashion, as long as it's finite" lol