- 22 Aug '04 17:35
*Originally posted by TheMaster37***Suspicions to be proven:**

**-IF such a function exists it has to be a polynomial to get rational output with rational input.**

Well, any ratio of two polynomials gives rational output with rational inpur (eg (x^3-9)/(x^2+3)). This doesn't necessarily give irrational output with irrationals, and the denominator may not have real roots.

**-Polynomials aren't irrational with every irrational input (eg there is always an irrational input wich given rational output)**

This is true. Note that irrational numbers can be associated with the degree of the lowest-degree polynomial of which they are a root. Are all irrationals roots of some polynomial? - 22 Aug '04 18:01 / 1 editTo 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