# What's the meaning of $\succ$ operator?

What is the meaning of $\succ$ symbol? I have an snippet which includes this operator: (Article is about choice theory)

"a complete and transitive preference $\succ$ over X"

• The same thing worded differently: Let $\succ$ be a complete and transitive preference over $X$. Jan 20, 2014 at 14:12

$\succ$ is named "succeeds" and is the name given by the author to the complete and transitive preference (~order). You can read it as a $>$ for simplification. Other uses of the symbol occur for example with matrices. $A\succ 0$ means that $A$ is a positive definite matrix (i.e. $x^T A x > 0 \quad\forall\ x\neq 0$)

• @SuatAtan happy to help. If this solved your question, please mark it as answered by clicking on the checkmark to the left of the answer. If not, feel free to ask for further clarification. Jan 22, 2014 at 18:05
• Unfortunately my reputation is not enough (<15) for voting. But after attaining this value i'll. Feb 21, 2014 at 9:10
• @SuatAtan Accepting answers doesn't fall within this restriction, see here for a description. Feb 23, 2014 at 13:25

Here is how you would find an explanation on the internet.

Entering the keywords "complete transitive preference choice theory," the first hit is this wikipedia page on preference. In the section basic premises, they start to define symbols for preference, and then in this later section they define what a complete and transitive preference order is.

I have a slight feeling you might be too focused on the symbol $\succ$ itself. The wording suggests you might believe that the symbol has one and only one meaning. This isn't a very practical viewpoint since many symbols have uses in different concepts, and sometimes the same concept uses multiple symbols. (In case my feeling completely wrong, I apologize in advance!)

Aside from the symbol $\succ$, an author could choose to use $>$ or anything else shaped like that. So the phrase

"a complete and transitive preference $\succ$ over X"

already completely explains what $\succ$ is: it is a complete and transitive preference over $X$. If one is still puzzled at this point, then the right question is what is a complete and transitive preference order? not "What's this symbol?" The symbol isn't that important, but what it denotes is important.

• Or if you see preference as something negative, you could chose $\prec$ or $<$; in fact about anything that has a "direction". Look over here for some examples. Jan 20, 2014 at 15:09
• Thanks rschwieb for your answer. Frankly, your advise about interpreting statements which have math symbols, is instructive for me. But as being newbie, suffocating in abstract terminology and sentences sometimes causes kind of obssession and misfocusing. So perhaps, this web app is great and like lighthouse for this reason. Thanks again. Jan 21, 2014 at 8:10
• @SuatAtan Awesome, then my gamble paid off! Don't worry, I think a lot of students hit the same snag. But I'm sure you'll rapidly get the hang of this thought pattern with practice. Jan 21, 2014 at 11:14