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text: 'The codomain $\\operatorname{cod}(f)$ of a [3jy function] $f : X \\to Y$ is $Y$, the set of possible outputs for the function. For example, the codomain of [3jv concat] is the set of all [3jr strings], and the codomain of the function $+$ is the set of all numbers.\n\nVisualizing a function as a map that takes every point in an input set to one point in an output set, the codomain is the output set (pictured on the right in blue in the image below).\n\n\n\nThe codomain of a function is not to be confused with the [3lh image] of a function, which is the set of points in $Y$ that can actually be reached by following $f$, and which may not include the whole set $Y$. For example, consider all the functions that take a [real_number real number] as input and produce another real number. Many of those functions cannot be made to produce every possible real number: For example, the function $\\operatorname{square} : \\mathbb R \\to \\mathbb R$ only produces non-negative numbers. For more on the distinction, see the page on [3lv codomain vs image].\n\n[fixme: Add a lens talking about how codomains are arbitrary but often natural/useful. Use example like how we can consider $+$ to have codomain $\\mathbb N$, $\\mathbb Z$, etc., and examples like Ackerman where the codomain "nat" makes by far the most sense (though "int" is fine too).]',
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