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  text: 'A [-3jy] $f: X \\to Y$ is *injective* if it has the property that whenever $f(x) = f(y)$, it is the case that $x=y$. Given an element in the [3lm image], it came from applying $f$ to exactly one element of the [3js domain].\n\nThis concept is also commonly called being "one-to-one".\nThat can be a little misleading to someone who does not already know the term, however, because many people's natural interpretation of "one-to-one" (without otherwise having learnt the term) is that every element of the domain is matched up in a one-to-one way with *every* element of the domain, rather than simply with *some* element of the domain.\nThat is, a rather natural way of interpreting "one-to-one" is as "[499 bijective]" rather than "injective".\n\n# Examples\n\n- The function $\\mathbb{N} \\to \\mathbb{N}$ (where $\\mathbb{N}$ is the set of [-45h natural numbers]) given by $n \\mapsto n+5$ is injective: since $n+5 = m+5$ implies $n = m$. Note that this function is not [4bg surjective]: there is no natural number $k$ such that $k+5 = 2$, for instance, so $2$ is not in the range of the function.\n- The function $f: \\mathbb{N} \\to \\mathbb{N}$ given by $f(n) = 6$ for all $n$ is not injective: since $f(1) = f(2)$ but $1 \\not = 2$, for instance.',
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