# elementary function and non-elementary function amount

#### shahar

##### Junior Member
What more bigger the group of elementary function or non-elementary function?

How can it will be proven?

#### HallsofIvy

##### Elite Member
First you will have to tell us how you wish to measure "bigger" for infinite sets! Both of the sets are infinite. For example. $$\displaystyle sin(\alpha x)$$ is an elementary function for all $$\displaystyle \alpha$$ and $$\displaystyle J_o(\beta x)$$ is a non-elementary function for all $$\displaystyle \beta$$.