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Definition: Let RealFun = R -> R.
. : R -> RealFun c(x) := c; +: (RealFun x RealFun) -> RealFun (f+g)(x) := f(x) + g(x); (f-g)(x) := f(x) - g(x); (f*g)(x) := f(x) * g(x); (f/g)(x) := f(x)/g(x); ..: (RealFun x Z) -> (R ->partial R) (fn)(x) := f(x)n; sqrt ( ): (Z x RealFun) -> (R ->partial R) (sqrtn(f))(x) := sqrtn(f(x));