Definition:Pointwise Addition of Real-Valued Functions
Jump to navigation
Jump to search
Definition
Let $f, g: S \to \R$ be real-valued functions.
Then the pointwise sum of $f$ and $g$ is defined as:
- $f + g: S \to \R:$
- $\forall s \in S: \map {\paren {f + g} } s := \map f s + \map g s$
where the $+$ on the right hand side is real-number addition.
Thus pointwise addition is seen to be an instance of a pointwise operation on real-valued functions.
Also see
- Pointwise Addition on Real-Valued Functions is Associative
- Pointwise Addition on Real-Valued Functions is Commutative
Sources
- 1961: I.M. Gel'fand: Lectures on Linear Algebra (2nd ed.) ... (previous) ... (next): $\S 1$: $n$-Dimensional vector spaces
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Exercise $\text{U}$
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): Chapter $1$: Rings - Definitions and Examples: $2$: Some examples of rings: Ring Example $8$
- For a video presentation of the contents of this page, visit the Khan Academy.