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,

is a super function. Also

is a super function. But

is not because

is not one of the basic functions on the list and also because division is not allowed in this defintion.

**Theorem:** Let

be a finite interval and let

be a super function. Then unless

is identically zero the equation

has only

**finitely** many solutions on the interval

.