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  "body": "\n## Example\n\nLet $F$ be a field, let $X$ be a set, and let $V$ be a [[vector space|000AYPA9AJ]] over $F$.\nThe set $V^X$ of all functions $f \\colon X \\to V$ is a vector space over $F$ with the pointwise operations\n$$(f + g)(x) = f(x) + g(x), \\qquad (af)(x) = a\\, f(x)$$\nfor $f, g \\in V^X$, $a \\in F$ and $x \\in X$.\nThe zero vector is the function with value $0$ at each point.\n\n## Remarks\n\nFor $X = \\{1, \\dots, n\\}$ and $V = F$, this is the [[coordinate space|0XM8BZD76G]] $F^n$.\nThe continuous functions $[0, 1] \\to \\R$ form a subspace of $\\R^{[0, 1]}$.\nIf $X$ is infinite and $V \\ne 0$, then $V^X$ is infinite-dimensional.\n\n## Explanations\n\n### L1 human\n\nWe add two functions by adding their values at each point.\nWe scale a function by scaling its values.\nWith these rules, functions behave like vectors, and the zero function is the zero vector.\n",
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