Absolute Value is Norm

Theorem
The absolute value is a norm on the set of real numbers $\R$.

Proof
By Complex Modulus is Norm then the complex modulus satisfies the norm axioms on the set of complex numbers $\C$.

Since the real numbers $\R$ is a subset of the complex numbers $\C$ then the complex modulus satisfies the norm axioms on the real numbers $\R$.

By Complex Modulus of Real Number equals Absolute Value then the absolute value satisfies the norm axioms on set of real numbers $\R$.