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Math Help - 1-1 corospondence

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    1-1 corospondence

    Hi. I have a problem that invovles proving a one to one corospondence. How do you go about proving the corospondence?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Chris11 View Post
    Hi. I have a problem that invovles proving a one to one corospondence. How do you go about proving the corospondence?
    f:X\mapsto Y\text{ is injective }\Leftrightarrow \left(f(x)=f(y)\implies x=y\right)\Leftrightarrow\left(x\ne y\implies f(x)\ne f(y)\right)
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    In words, if different inputs always give different outputs. More formally, If we suppose f: A \rightarrow B has the property that if a,a' \in A and a \neq a', then f(a) \neq f(a'). We say f is 1-1 or injective or monic.

    Another way of saying that is to observe that \forall a,a' \in A, if f(a)=f(a') then a = a'.
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