Domain of Real Square Function

Theorem

The domain of the real square function is the entire set of real numbers $\R$.

Proof

The operation of real multiplication is defined on all real numbers.

Thus:

$\forall x \in \R: \exists y \in \R: x^2 = y$

Hence the result by definition of domain.

$\blacksquare$

Sources

• 1964: William K. Smith: Limits and Continuity ... (previous) ... (next): $\S 2.2$: Functions