Timeline for Is it possible to give, in economics, an example of a relation ( set of ordered pairs) that is not a function?
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| Apr 19, 2019 at 20:08 | vote | accept | CommunityBot | ||
| Apr 19, 2019 at 17:30 | comment | added | Martin Van der Linden | Sure. Every relation $R \subseteq (A\times B)$ can be somewhat "equivalently" represented as a function $f \colon A \rightarrow 2^B$ such that for all $a \in A$ and all $b \in B$, we have $b \in f(a)$ if and only if $(a,b) \in R$. It remains that $\succ$ is not itself a function. I think it's fair to say that binary relations like $\succ$ are "useful" in economics. Since the OP's question was about "relations that are not functions and are useful in economics" that hopefully provides a good example. | |
| Apr 19, 2019 at 16:50 | comment | added | John Doucette | Example 1 can be represented as a function though, relating the set of alternatives $S$ to the powerset of $S$. It is not very unusual to see it represented this way. It's perfectly fine (mathematically) to have a function relate elements to sets. It's just not a function from the set to itself in that case. Example 2 has the same issue. | |
| Apr 19, 2019 at 13:19 | history | edited | Martin Van der Linden | CC BY-SA 4.0 |
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| Apr 19, 2019 at 13:10 | history | edited | Martin Van der Linden | CC BY-SA 4.0 |
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| Apr 19, 2019 at 12:59 | history | edited | Martin Van der Linden | CC BY-SA 4.0 |
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| Apr 19, 2019 at 12:51 | history | answered | Martin Van der Linden | CC BY-SA 4.0 |