Originally Posted by

**ThePerfectHacker** I came up with a theorem.

Define a __super function__ to be a function defined for all real numbers that is made out of sum/difference or product (not quotient) or composition of: sines,cosines,exponentials,polynomials.

For example, $\displaystyle \sin (e^x + 2x)$ is a super function. Also $\displaystyle \sin (\cos (\sin e^{x^2+x})))$ is a super function. But $\displaystyle \sin (1/x)$ is not because $\displaystyle 1/x$ is not one of the basic functions on the list and also because division is not allowed in this defintion.

**Theorem:** Let $\displaystyle I$ be a finite interval and let $\displaystyle f(x)$ be a super function. Then unless $\displaystyle f(x)$ is identically zero the equation $\displaystyle f(x) = 0$ has only **finitely** many solutions on the interval $\displaystyle I$.