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Is there any difference between an injective function and a function that maps A into B? If yes, does the difference consist in the fact that a function that maps A into B can fail to be one-to-one, whereas an injective function is always a one-to-one function?

Thanks a lot

Fish

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You're right.

We say $f$ maps $A$ into $B$ if $f$ is a function whose domain is (or sometimes contains) $A$, and the image of $A$ under $f$ is (or sometimes is contained in) $B$.

We say $f$ is injective if for any two outputs in the image of $f$, they are guaranteed to have come from two different inputs in the domain of $f$.


This is one of the annoying bits of notation. An "onto" function is surjective, but there's no such thing as an "into" function. This lack of notational symmetry is why I avoid the term "onto".

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