"Either value can be higher"?

Question

I'm writing a math paper and want to say that two quantities, a*b and (a-b), cannot  be ranked in a unique way. Depending on the values a and b, either can be higher.

My idea is to say "either value can be higher" or "either of the two values can be higher".

As a non-native speaker, I check my ideas with google - whether I get many hits when search for  the exact sentences. Surprisingly, though both sentences above seem very normal to me, and it seems the point I'm trying to make  ("either can be higher") should  arise in many contexts, I get zero hits with both above sentences.

So, what's the succinct way of saying that "For some values a and b, a*b higher that (a-b), and for some values, the reverse inequality is true".

Thanks a lot!

Ram Pillai · Answer

When one says, "either side of the coin", it means "both sides". Here either is an adjective. In "either of the sides", it refers to one of the two sides. Here, either works like a pronoun.

DJClayworth · Answer

In general "either value can be X" (X being an adjective) is perfectly normal and generally understandable, meaning that one of the values or the other can be X. "Either of the two values..." puts a slight emphasis on the fact that there are exactly two (which is normally implied by the use of 'either', but is not always understood), but doesn't really add anything to the meaning.

You are laying yourself open to an ambiguity, which is that you don't specify "higher than what?". Your sentence could be taken to mean "either of the values could be higher than it is".

I would recommend "Either of the values could be higher than the other."

Jason Bassford · Answer

To avoid confusion, you could simply say this:

The values can be unequal. OR
  The values need not be equal.

If you're trying to say that one will always be higher than the other (it's not clear from the question), then say this:

The values must be unequal. OR
  The values must be different.

By definition, if the values are not the same, then one of them has to be higher than the other. But this wording avoids the potential ambiguity of the original version.

"Either value can be higher"?

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