# Using the word “difference” in the meaning “result of subtraction” taking into account the negative values

The result of subtraction is called "difference". At first glance it might seem that it shouldn't cause an ambiguity over the value denoted by this word; until we stumble upon subtractions that produce negative results.

What do I actually mean? It is clear that:

2 − 5 = −3

But when we say "the difference between 2 and 5" don't we mean "3" in the first place irrespective of the order in which we place the numbers in the sentence? What expression should we use to make it clear, regardless of the context, that we imply "−3"?

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"The difference between 2 and 5" is not the same as "2 minus 5". The former describes magnitude, the latter describes magnitude and direction. – J.R. Dec 21 '12 at 16:44
That's what happens when you allow modern radicals to intrude their novelties upon Classical purity, in math no less than language. :) In writing, −3 is unambiguous; in speech, “minus three”. But it's a question for mathematicians, not philologists, to tell us whether the difference (as opposed to the result) is minus three or absolute three. – StoneyB Dec 21 '12 at 16:46
Or "negative three". – MετάEd Dec 21 '12 at 16:55
In maths, the difference between two real numbers x and y is defined as the absolute value of x-y. x-y is just called x-y (x take / minus y) - there isn't a universally agreed term (though I think 'directed difference' may have been used). – Edwin Ashworth Dec 21 '12 at 17:58
@StoneyB The phrase "_ and _" is symmetric in its arguments, and adding in a "between" doesn't change this, but subtraction is not symmetric in its arguments. For this reason, in mathematics, we don't use this phrase due to its imprecision (unless we're simultaneously pointing at a scrawl on a blackboard that clarifies, or unless there's some reason we don't care about sign). :) I recommend non-mathematicians do likewise, but when I stumble across the phrase "the difference between _ and _", I usually interpret it as what J.R. and Edwin said. – Billy Dec 21 '12 at 19:31