Recent content by itznogood

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    Set of all one-to-one mappings of a non empty set onto itself

    I think A(S) has to be set of all bijections from S--->S. Because on the next page Herstein lists properties of A(S). He says for any element σ in A(S) , there exists an element σ^{-1} in A(S). I guess, an inverse mapping is possible only for bijective maps. I hope I am right ...
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    Set of all one-to-one mappings of a non empty set onto itself

    Yup, that's what. "S to itself" , "S--->S" all these are ok. And yes I am concerned about cases when S is infinite . Coz for finite set S the mapping "S--->S" if it is injective will be surjective too and hence also bijective. But for the infinite case this may not be so.Hence I want to make...
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    Set of all one-to-one mappings of a non empty set onto itself

    Herstein in his book topics of algebra(sec 1.2, 2nd ed) defines A(S) to be set of all one-to-one mappings of S onto itself, S is a non empty set. Is he defining A(S) to be set of all bijections from S-->S or is he defining A(S) to be set of all injections from S--->S. He uses the word...