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I have these two statements:\

(i). If $A>0$, the left object touches the right object for $B>0$

(ii). If $A<0$, the right object touches the left object for $B<0$

How can I write these statements in a compact form in only one statement? Which one of these is correct?

  1. If $A>0$ ($A<0$), the left (right) object touches the right (left) object for $B>0$ ($B<0$).
  2. If $A>0$ ($A<0$), the left (respectively, right) object touches the right (respectively, left) object for $B>0$ (respectively, $B<0$).
  3. If $A>0$ (respectively, $A<0$), the left (respectively, right) object touches the right (respectively, left) object for $B>0$ (respectively, $B<0$).
sara96
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    all three options are far more confusing than writing out (i) and (ii) separately. – Matthew Towers Jul 31 '22 at 12:16
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    Agree with @MatthewTowers. Compact writing is a minor goal; clear writing is the major goal. We should write with such clarity that a reader can get the meaning from a single read of the sentence (not going back and reading it multiple times). I would almost never use these hard-to-read constructions, especially when simply writing the two versions is extremely clear. – Greg Martin Jul 31 '22 at 19:54
  • The first statement is correct as I've seen that notation used quite frequently in many course books. – VizDracViz Jul 31 '22 at 12:45

1 Answers1

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How can I write these statements in a compact form in only one statement?

You need to make explicit how the two objects depend on A and on B. Also, it's not clear from the original statements that 'touch' is not a symmetric relationship, which your 3 options suggest.

Without further context, "if the nonzero reals $A$ and $B$ have the same sign, then the left and right objects touch each other" is to me the most reasonable 'compactification', but from your 3 options I'm guessing that this is not what your original statements actually mean.

Which one of these is correct?

Option #1 is the clearest. I don't think options #2 and #3 are correct, because when specifying a correspondence between two lists, the word "respectively" should appear only once.

ryang
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