Domain of Real Square Root Function

Theorem

The domain of the real square root function is the set of positive real numbers $\R_{\ge 0}$:

$\set{x \in \R: x \ge 0}$

Proof

From Square of Real Number is Non-Negative:

$\forall x \in \R: x^2 \ge 0$

Hence the result by definition of domain.

$\blacksquare$

Sources

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