elementary function and non-elementary function amount

[shahar]

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

How can it will be proven?

 

[HallsofIvy]

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 $\displaystyle \beta$.