If I say
the difference between $x$ and $y$
Does that mean $x - y$ or $y - x$ or $|x - y|$?
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1It depends. ${}$ – Mariano Suárez-Álvarez Sep 08 '13 at 02:19
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What does it depend on? – Lemon Sep 08 '13 at 02:20
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2On what you mean! – Mariano Suárez-Álvarez Sep 08 '13 at 02:20
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But I meant what I stated. – Lemon Sep 08 '13 at 02:20
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1What you stated does not mean anything unambiguosly, so it cannot mean that. – Mariano Suárez-Álvarez Sep 08 '13 at 02:20
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4Clearly, you understand that the phrase is ambiguous, so it is quite unclear what you are after. The only sensible suggestion is: just do not say that. – Mariano Suárez-Álvarez Sep 08 '13 at 02:21
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It's worth noting that because there's an easier way to say $x-y$ (namely "$x$ minus $y$"), your best bet when reading something like this is to go with the interpretation of Andreas Blass and T. Bongers. – Mark S. Dec 14 '13 at 20:33
2 Answers
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If I were to say "the difference between $x$ and $y$," I would probably mean $|x-y|$, simply because the use of "between" suggests symmetry between $x$ and $y$.
Andreas Blass
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As Mariano pointed out, the meaning is somewhat ambiguous and subjective. It pretty much never hurts to add a word or two of clarification. If I personally use it, I'm usually referring to the difference in absolute terms, so $|x - y|$.