How to write "at least one of these two is greater than..." in mathematical notation?

Question

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?

Max · Accepted Answer · 2020-04-26T07:24:15.973

1

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?

edited Apr 26 '20 at 07:24

answered Apr 26 '20 at 07:15

Max

14,233

This certainly seems to work, thank you! – uhoh Apr 26 '20 at 07:24
But I still wish there was a way to say "both greater than $E$ and at least one greater than $E + \Delta E$" – uhoh Apr 27 '20 at 12:45
2

You could just say that. Despite appearances to the contrary, most mathematicians understand words. – Max Apr 27 '20 at 13:26
ya that might be what I'll do in the end, thanks! – uhoh Apr 27 '20 at 13:37

How to write "at least one of these two is greater than..." in mathematical notation?

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