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Is it possible to convert a one-to-many function to a one-to-one function.
The input is going to be unique and hence the out of the function should also be unique.
Repeating output would only create more ambiguity when the reverse mapping is to be done.
I hope the question makes some sense.
Thanks in advance.

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    One way to create a genuine function from a one-to-many relation is to enlarge the "domain". For example, if you have a one-to-many binary relation $R$ which is a subset of $X\times Y$ (so $X$ might be thought of as the "domain" of $R$) then there's a natural function $f\colon R\to Y$ given by $f((x,y))=y$. You could think of the passage from $R$ to $f$ as fattening up the domain from $X$ to $R$.2011-04-15
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    Or something else you could do is to change the "codomain" to the power set of $Y$: define $g:X\to \mathcal{P}(Y)$ by $g(x)=\{ y\in Y\colon (x,y)\in R\}$. I guess one nice thing about both of these is that you don't lose any information: you can recover $R$ from both $f$ and $g$.2011-04-15
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    A one-to-many "function" is a one-to-one function from your domain into a space of sets.2011-04-15
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    What is the domain/range of your function/relation? discrete? over integers? over reals? continuous? any other details that might help?2011-04-16

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