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In some problems, one is asked to determine if the entity on the left hand side is greater than, less than, or equal to the entity on the right hand side. Is there a mathematical symbol to denote this? A proof in this case might proceed like:

To prove that a <the symbol> b i.e. to prove that ...

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    $\begingroup$ This info is packed in the value of $\text{sgn}(a-b)$, the signum of $a-b$. $\endgroup$
    – kimchi lover
    Commented Jan 7, 2019 at 1:33
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    $\begingroup$ What's wrong with "Is $a\gt b$ or is $a \lt b$ or is $a=b$?", and then proving that one and only one of those options must hold., and which one actually holds. $\endgroup$
    – amWhy
    Commented Jan 7, 2019 at 1:35
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    $\begingroup$ It's irritating but no there is no standard notation. But there's nothing wrong with saying "I will use the symbol BLAH to mean whichever of the relations, >,<, or = applies between terms. Now $2x + 5 BLAH 10a + 7$ if and only if $x BLAH 5a + 1$ so ....." $\endgroup$
    – fleablood
    Commented Jan 7, 2019 at 1:40
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    $\begingroup$ As has been pointed out, you could use $\text{sgn}(a-b)$ if space is limited. However, it is far better just to say something like "let's prove which of $a$ and $b$ is larger, or if they are equal." That's far more readable. Frankly, I wouldn't even use the $>$/$<$/$=$ symbols. $\endgroup$
    – Ben W
    Commented Jan 7, 2019 at 1:44
  • $\begingroup$ Agree with others. Just use words. Mathematics doesn't always need to be decorated with strange symbols. And if the strange symbols reduced readability and comprehension, they should definitely not be used. $\endgroup$
    – bubba
    Commented Jan 7, 2019 at 4:41

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There is a symbol for comparability (in the context of posets for example): $\overset{<}{\underset{>}{=}}$.

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  • $\begingroup$ Given the context, we might want to put a question mark on top of all that. $\endgroup$
    – Ivan Neretin
    Commented Mar 23 at 6:41

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