An injection, or "one-to-one function," is a function that takes distinct values on distinct inputs. Equivalently, an injection is a function for which every value in the range is the image of exactly one value in the domain.
Alternative definition: A function is an injection if for all , if then .
The binary relation iff there is an injection forms a partial order on the class of cardinals: , and implies by the Cantor-Schroeder-Bernstein theorem, and and implies because the composition of injections is again an injection.
Linear functions are injections: , , . The domain choosing is also important. For example, while , is not an injection (), the function , , is an injection.
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