I've seen someone asking a question with $\gneq$ ($\gneq$
) in it. What does it mean? What's the difference with $\geq$ ($\geq$
)?
What is $\gneq$?
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0We need the context. When writing $A \gneq B$, what are $A,B$? Maybe there is some meaning defined for rather frugal loopoids $A,B$ and $A \gneq B$ and $A \ge B$ have different meanings... So we must await the return of Oltarus to find the source. – 2011-12-08
2 Answers
I would think $\gneq$ means exactly the same as $>$, i.e. it would mean greater than and not equal to (while the symbol $\geq$ means greater than or equal to). But of course there may be some specialized use where it doesn't mean this though; everything depends on context.
In the context of the question you linked to, I can say with certainty that the intended meaning is the one above. That is,
$n\gneq 3 \iff n>3 \iff n\text{ is greater than }3$ and, because $n$ is an integer in this context, we can also say that $n\gneq 3\iff n\geq 4.$
As Rasmus points out below, the analogous notations with set inclusion, $\subset$ vs. $\subsetneq$, unfortunately do not mean the same in general; many authors use $A \subset B$ to mean "$A$ is a subset of $B$, and could be equal to $B$". An unambiguous alternative to express that would be to write $\subseteq$.
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0@ZevChonoles : "OP asked that what is the difference between $\gneq$ and $\ge$, but your answer was primarily explaining the similarity between $\gneq$ and $gt$ ( recently you added something in the answer present in brackets ) , but the point I was stressing was that "OP might have thought to ask the difference between the $\gneq$ and $gt$ but used "$\ge$ " instead of "$\gt"$, if the question is re-edited it would make much sense, but the question present in the above form is universally known as everyone knows the difference between $\gneq$ and $ge$. You understood my point ? – 2011-12-08
$ a \geq b$ means that $a$ is greater than $b$ or it can be equal to $b$.
$a \gneq b$ means $a$ is greater than $b$ and it can't be equal to $b$.
The $\gneq$ sign used when we want to emphasis that they can't be eqaul.
for example I can write $x^2 +1 \geq 0$ and it is true because it means $x^2 +1$ is greater than zero or it can be equal to zero. (I hope you remember how the or operator works.)
but it is better to say that $x^2 +1 \gneq 0$ which means $x^2 +1$ is greater than zero and it can't be zero.
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0@Bardia : do it now ! , nice example, I was waiting for such practical application, really practical situation to contrast their usage, I searched in google for much time, but didn't found any such examples or situations. – 2011-12-08