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

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?

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?

• This certainly seems to work, thank you!
– uhoh
Apr 26, 2020 at 7:24
• 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, 2020 at 12:45
• You could just say that. Despite appearances to the contrary, most mathematicians understand words.
– Max
Apr 27, 2020 at 13:26
• ya that might be what I'll do in the end, thanks!
– uhoh
Apr 27, 2020 at 13:37