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2023-11-01 08:55:40 +00:00
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image = range
codomain: set that a function is stated to evaluate to; range: values that are possible from a function
onto function: surjection
bijective: injective & surjective
injective: \forall x, y \in \operatorname{Domain}.~ f(x) = f(y) \implies x = y \tag{one-to-one}
surjective: \forall y \in \operatorname{Codomain}.~\exists x \in \operatorname{Domain}.~ f(x) = y \tag{codomain = range}
inverse only a function for bijective functions - not surjective means undefined for some values of the domain, not injective means multi-valued for some values of the domain