Sum of Sequentially Computable Real-Valued Functions is Sequentially Computable

Theorem

Let $D \subseteq \R^n$ be a subset of real cartesian $n$-space.

Let $f, g : D \to \R$ be sequentially computable.

Then, $h : D \to \R$ defined as:

$\map h \bsx = \map f \bsx + \map g \bsx$

is sequentially computable.

Proof

Follows immediately from:

• Real Addition is Sequentially Computable
• Composition of Sequentially Computable Real-Valued Functions is Sequentially Computable

$\blacksquare$