Functions form a Vector Space

Functions can be treated as infinite dimensional vectors. For example, typically a vector is interpreted as an ordered list of numbers. This could also be interpreted as a function mapping the indices to the values. E.g. a vector in $\mathbb{R}^3$ can be considered to be a function mapping the domain $1, 2, 3$ to the codomain $\mathbb{R}$ (since the values in the vector are real numbers). $$ v:…