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

<p>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.</p>

CC BY-SA 3.0
2018-01-24T14:05:37.037Z
Thanks for the help. I was along those lines, but felt the proof is much longer than that, i suppose.
JadoM
CC BY-SA 3.0
2018-01-24T06:30:59.697Z
2018-01-24T06:30:59.697Z
Norman
<p>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. </p>

<consumer-theory>
Show that strict preference ordering is not reflexive
JadoM
# Show that strict preference ordering is not reflexive

(Asked by: username_0 on 2018-01-24)

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.

**Tags:** consumer-theory


---

## 1 answers

### Answer by username_1 on 2018-01-24. Score: 1

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.

> **Comments:**
> **username_0**: Thanks for the help. I was along those lines, but felt the proof is much longer than that, i suppose.  

---

