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A bijective function, also known as a bijection, is a type of function between two sets, where each element in the domain (input) set is paired with exactly one element in the codomain (output) set, and vice versa. In other words, a bijective function establishes a one-to-one correspondence between the elements of the domain and the elements of the codomain.
Formally, a function f:A→Bf:A→B is bijective if and only if:
In simpler terms, a bijective function is both injective (or one-to-one) and surjective (or onto). It means that each element in the codomain is paired with exactly one element in the domain, and there are no "extra" elements left in either set without a corresponding match in the other set.
Graphically, a bijective function can be represented by a plot where each input value has a unique corresponding output value, and there are no horizontal or vertical line tests that intersect the graph at more than one point.
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