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The book I am currently reading, is written in a local language, uses the symbol $$\gtreqqless$$

Noted usage in the book (translated):

Let $f(x) = x^3e^{-3x}$ for x > 0. Then what is the maximum value of $f(x)$ ?

Solution : $\dotsc$ $f'(x) = 3e^{-3x}x^2(1-x)$... We have to work explicitly with $1 - x$ since $3e^{-3x}$ is positive for x > 0 $\therefore$ We have to see when 1 - x $\geqslant$ 0 and when 1 - x $\leqslant$ 0. We can see that 1 - x $\gtreqqless$ 0 $\Longleftrightarrow$ 1 $\gtreqqless$ x $\dotsc$

So how is the symbol read ,or, What does it mean ?

Edit: I have searched through the book and it does not provide any page on symbols used and no past explanation has been provided.

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    $\begingroup$ It just means that if you place any of the three symbols ($=,>,<$) at both equations, the equivalence holds. It is basically a shortcut for writing $1-x>0\Leftrightarrow 1>x,\ 1-x=0\Leftrightarrow 1=x$ and $1-x<0\Leftrightarrow 1<x$. $\endgroup$ Jul 3 at 15:49
  • $\begingroup$ @StefanAlbrecht I see. Feel free to add it as an answer so I can accept it. $\endgroup$
    – Krosin
    Jul 3 at 15:52
  • $\begingroup$ There are two answers already, which essentially convey the same thing, you can accept either of them (your preference), or if @StefanAlbrecht wishes, he can post one. $\endgroup$ Jul 3 at 16:00
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    $\begingroup$ It is not too difficult to guess what it means, but how you read it is another story... I would be interested to have the opinion of a native English speaker... $\endgroup$
    – J.-E. Pin
    Jul 3 at 16:25
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    $\begingroup$ @J.-E.Pin One possible reading is, "One minus $x$ is greater than, equal to, or less than zero if and only if one is (respectively) greater than, equal to, or less than $x.$" $\endgroup$
    – David K
    Jul 3 at 17:12
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It is similar to $\pm$, so for example, $(a\pm b)^2=a^2\pm 2ab+b^2$, if you take a plus you take it everywhere, if you take a minus, you take it everywhere.

Likewise, if you consider $1-x>0$, you have $1>x$. (Here, we took the topmost symbol!)

If you have $1-x=0$, it means $1=x$; here we took the second symbol $=$. You can see the pattern now.

Hope this helps. Ask anything if not clear :)

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    $\begingroup$ Thank you for the explanation as well! $\endgroup$
    – Krosin
    Jul 3 at 16:05
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It's a shorthand notation for $$ 1-x > 0 \iff 1 > x \quad\text{and}\quad 1-x = 0 \iff 1 = x \quad\text{and}\quad 1-x < 0 \iff 1 < x \, . $$

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  • $\begingroup$ Thank you for the answer :) $\endgroup$
    – Krosin
    Jul 3 at 16:05

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