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If I say

the difference between $x$ and $y$

Does that mean $x - y$ or $y - x$ or $|x - y|$?

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    $\begingroup$ It depends. ${}$ $\endgroup$ – Mariano Suárez-Álvarez Sep 8 '13 at 2:19
  • $\begingroup$ What does it depend on? $\endgroup$ – Hawk Sep 8 '13 at 2:20
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    $\begingroup$ On what you mean! $\endgroup$ – Mariano Suárez-Álvarez Sep 8 '13 at 2:20
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    $\begingroup$ What you stated does not mean anything unambiguosly, so it cannot mean that. $\endgroup$ – Mariano Suárez-Álvarez Sep 8 '13 at 2:20
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    $\begingroup$ Clearly, 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. $\endgroup$ – Mariano Suárez-Álvarez Sep 8 '13 at 2:21
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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 $y$.

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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 $|x - y|$.

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