<p>Let <span class="math-container">$\succsim$</span> complete and <span class="math-container">$x, y, z \in X$</span>. Suppose <span class="math-container">$x \succsim y$</span> and <span class="math-container">$y \succsim z$</span>. Is it OK to write <span class="math-container">$x \succsim y \succsim z$</span> just knowing this?</p>

<p>Or, on the contrary, such expression automatically implies <span class="math-container">$x \succsim z$</span>?</p>

CC BY-SA 4.0
2019-10-01T17:37:09.833Z
This seems more like a math question. (Math notation specifically, so very little microeconomics is involved.) Also, it boils down to whether writing
$$
5 > 2 < 3
$$
is okay. These are two different inequalities, but I was lazy and did not write the symbol 2 again. But this clearly does not imply anything about the relationship of 5 and 3.
Giskard
CC BY-SA 4.0
2019-10-01T21:11:57.020Z
Strictly speaking, $\succsim$ symbolizes a ***binary*** relation, and so should be used as one. Writing "$x\succsim y\succsim z$" as a shorthand for "$x\succsim y$ and $y\succsim z$" is an abuse of notation and should only be used within an appropriate context where confusion/misinterpretation is unlikely.
Herr K.
CC BY-SA 4.0
2019-10-02T16:45:30.013Z
To be clear, you can't conclude that $x \succsim z$ without assuming transitivity.
Art
<microeconomics>
Notation: is it correct to write $x \succsim y \succsim z$ before using transitivity?
econ86
# Notation: is it correct to write $x \succsim y \succsim z$ before using transitivity?

(Asked by: username_0 on 2019-10-01)

Let $\succsim$ complete and $x, y, z \in X$. Suppose $x \succsim y$ and $y \succsim z$. Is it OK to write $x \succsim y \succsim z$ just knowing this?

Or, on the contrary, such expression automatically implies $x \succsim z$?

**Tags:** microeconomics
> **Comments:**
> **username_1**: This seems more like a math question. (Math notation specifically, so very little microeconomics is involved.) Also, it boils down to whether writing $$ 5 > 2 < 3 $$ is okay. These are two different inequalities, but I was lazy and did not write the symbol 2 again. But this clearly does not imply anything about the relationship of 5 and 3.  
> **username_2**: Strictly speaking, $\succsim$ symbolizes a ***binary*** relation, and so should be used as one. Writing "$x\succsim y\succsim z$" as a shorthand for "$x\succsim y$ and $y\succsim z$" is an abuse of notation and should only be used within an appropriate context where confusion/misinterpretation is unlikely.  
> **username_3**: To be clear, you can't conclude that $x \succsim z$ without assuming transitivity.  

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## 0 answers

