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Proving that Every preference relation can be represented by utility function

Let $X=\{x_1,\dots, x_n\}$, we will use induction on size of $X$ to prove that utility representation exists. Base step $(|X|=1)$: In the base step $X=\{x_1\}$ and so utility representation exists ...
mynameparv's user avatar
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Proving that Every preference relation can be represented by utility function

The following is a nice proof from Osborne and Rubinstein's Models in Microeconomic Theory. We want to prove that Every preference relation on a finite set can be represented by a utility function. ...
Riccardo Iorio's user avatar

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