Functions such as $ \sin(x) $ are considered to be elementary, however functions like $ \text{erf}(x) $ are considered to be non-elementary.
What makes elementary functions different from non-elementary functions, both $ \sin(x) $ and $ \text{erf}(x) $ can only be expressed as an infinite sum containing the 4 basic operations, division, multiplication, addition, and subtraction. Is what makes a function elementary a purely arbitrary decision?
