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I want to write the following in standard mathematical notation.

All integers $i, j$ such that $f(i, j) > E$ and $f(k, l) > E + \Delta E$ or $f(i, j) > E + \Delta E$ and $f(k, l) > E$

where $f$ monotonically increases with the square of each integer and $E$ and $\Delta E$ are both positive. It could be also written

$f(i, j), f(k, l) > E$ and at least one of $f(i, j)$ or $f(k, l)$ are $> E + \Delta E$.

I'm looking for an easy to read way to write this, not something that involves multiplication or some other technique that enforces this constraint mathematically but might take a while for some to understand how.

Is there an easy way to write this "...at least one of these two expressions is greater than...?" requirement?

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The inequalities in your original post don't seem to be equivalent, but with the new ones not something like $max(f(i, j), f(k, l))>E+\Delta E$, $min(f(i,j), f(k, l))>E$ or similar?

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  • $\begingroup$ This certainly seems to work, thank you! $\endgroup$
    – uhoh
    Apr 26, 2020 at 7:24
  • $\begingroup$ But I still wish there was a way to say "both greater than $E$ and at least one greater than $E + \Delta E$" $\endgroup$
    – uhoh
    Apr 27, 2020 at 12:45
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    $\begingroup$ You could just say that. Despite appearances to the contrary, most mathematicians understand words. $\endgroup$
    – Max
    Apr 27, 2020 at 13:26
  • $\begingroup$ ya that might be what I'll do in the end, thanks! $\endgroup$
    – uhoh
    Apr 27, 2020 at 13:37

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