Pointwise Difference of Simple Functions is Simple Function

Theorem
Let $\left({X, \Sigma}\right)$ be a measurable space.

Let $f,g : X \to \R$ be simple functions.

Then $f - g: X \to \R, \left({f - g}\right) \left({x}\right) := f \left({x}\right) - g \left({x}\right)$ is also a simple function.

Proof
By Scalar Multiple of Simple Function is Simple Function, $- g = -1 \cdot g$ is a simple function.

By Pointwise Sum of Simple Functions is Simple Function, so is $f - g$.