Go backward to Go up to Top Go forward to Example

Pointwise Function Definition

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));