Given a relation $R$ between $A$ and $B$, what properties does $R$ have to satisfy for $R=\operatorname{graph}(f)$ for some function $f:A\to B$?
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To every elements in $a \in A$, there is a unique element in $b \in B$ such that $aRb$? – user614287 Dec 10 '18 at 05:04
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What does "graph(f)" mean? – Acccumulation Dec 10 '18 at 05:11
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@Acccumulation The graph of a function $f:A \to B$ is the set ${(x, f(x)) : x \in A }$. – Patrick Stevens Dec 10 '18 at 05:19
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You need two properties.
1) For each $x\in A$ there is a $y\in B$ such that $(x,y)\in R$
2) If $(x_1,y_1)\in R$ and $(x_2,y_2)\in R$, then $$x_1 = x_2 \implies y_1=y_2$$
Mohammad Riazi-Kermani
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I think the second point is a bit unclear. Perhaps rewrite it as "If $(x,y_1), (x,y_2) \isin R$ then $y_1=y_2$"? – Acccumulation Dec 10 '18 at 05:25
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