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How do i show that the strict preference (>) ordering is not reflexive. I've tried to prove this by asymmetry but I am not sure this is the way to do it. Any help? Thank You.

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Just think about the definition of $\succ$ (in terms of $\succeq$) and the result follows immediately.

Proof: Suppose $x\succ x$. Then, by definition, $x\succeq x$ and $x\nsucceq x$, which is impossible. Hence, $x\nsucc x$ which means that $\succ$ is not reflexive.

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  • $\begingroup$ Thanks for the help. I was along those lines, but felt the proof is much longer than that, i suppose. $\endgroup$ – JadoM Jan 24 '18 at 14:05

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