Category:Real-Valued Functions

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This category contains results about Real-Valued Functions.
Definitions specific to this category can be found in Definitions/Real-Valued Functions.

Let $f: S \to T$ be a function.

Let $S_1 \subseteq S$ such that $\map f {S_1} \subseteq \R$.


Then $f$ is said to be real-valued on $S_1$.


That is, $f$ is defined as real-valued on $S_1$ if and only if the image of $S_1$ under $f$ lies entirely within the set of real numbers $\R$.


A real-valued function is a function $f: S \to \R$ whose codomain is the set of real numbers $\R$.

That is, $f$ is real-valued if and only if it is real-valued over its entire domain.