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I have seen things like \lessgtr $\lessgtr$ (less on top, greater on bottom;) being used in paper. Can someone give me an example of how a double inequality is used?

RobPratt
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Superman
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    When I have seen this, it's used in a similar way as $\pm$ and $\mp$, where the two "tops" correspond and the two "bottoms" correspond. – nomen Feb 12 '20 at 17:44
  • Like, can you give me a specific example? – Superman Feb 12 '20 at 17:45
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    As for "I am not too sure how to type math formulas here"... see the MathJax Tutorial. All you need to do for yours here is simply enclose it in dollar signs., $\lessgtr$ produces $\lessgtr$. – JMoravitz Feb 12 '20 at 17:46
  • @JMoravitz got it, thank you! – Superman Feb 12 '20 at 17:47
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    Does this answer your question? What is $\gtrless$? – JMoravitz Feb 12 '20 at 17:48
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    For example, we have $a\lessgtr b\iff -a\gtrless -b$. – Berci Feb 12 '20 at 18:02
  • @JMoravitz that’s one example, I may need to see more examples so I can get a better idea of how it’s used – Superman Feb 12 '20 at 18:09
  • @Berci well that’s a very simple example. I was looking for a more concrete example that is commonly used in “common” mathematics like trig, calculus, linear algebra, etc – Superman Feb 12 '20 at 18:10
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    In my experience this symbol is not "commonly used" in "common" mathematics... – JMoravitz Feb 12 '20 at 18:12
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    It should be clear in context. I'd interpret $a \lessgtr b$ to mean "either $a < b$ or $a > b$ but we don't know which". This could be useful for proving a statement such as "If $0 < a <b$ then $\sqrt{a}< \sqrt{b}$". Proof: $\sqrt{a}\lessgtr \sqrt{b}\implies a=\sqrt{a}\sqrt{a}\lessgtr\sqrt{b} \lessgtr \sqrt{b}\sqrt{b}=b\implies a\lessgtr b$. As we know $a < b$ it must be $\sqrt{a}<\sqrt{b}$". We can do multiple cases at once when the logic is the same. – fleablood Feb 12 '20 at 18:41

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