Domain of Real Square Function
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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