English Language & Usage Asked by user32606 on March 9, 2021
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”?
The only expression that always means "−3", regardless of context, is "−3". Likewise, the only way to make clear that you mean not just "the difference between 2 and 5" but "2 − 5", is by flat out saying "two minus five".
Incidentally, that's what they ask you in school, "How much is two minus five?" And not "What is the difference between two and five?"
Correct answer by RegDwigнt on March 9, 2021
Neither RegDwigнt's answer nor the comments to the question itself provide a citation to any authority for their apparent view that (a) "difference" means the absolute value (i.e., magnitude) of the result of a subtraction, rather than a signed number or (b) that it does not matter whether you say "the difference of A and B" or "the difference of B and A" because, in their view, these are equivalent assertions.
Apparently not!
Wolfram MathWorld's article on "Subtraction" states:
Subtraction is the operation of taking the difference d=x-y of two numbers x and y. Here, x is called the minuend, y is called the subtrahend, and the symbol between the x and y is called the minus sign. The expression "x-y" is read "x minus y."
This asserts that "the difference of x and y" is "x - y" and thus "difference of" does indeed imply a ordered relation between the two entities that follow.
Wolfram's MathWorld is a reputable source on all things mathematical.the
Answered by Jim Ratliff on March 9, 2021
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