# The word “and”.

If I say

the difference between $x$ and $y$

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

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

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 $y$.
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 $|x - y|$.