I am writing an academic paper with a choice of titles:

  1. On the equivalence of A and B

  2. On the equivalence between A and B


  1. On the equivalence of A, B and C

  2. On the equivalence between A, B and C

  3. On the equivalence among A, B and C

where A,B,C are some scientific or math notions.

Should I use of or between or among? Which case is more correct or suitable?

  • 3
    Let's stick with two, OK? The first two suggest a different emphasis. (1) is a demonstration that A and B are equivalent, while (2) is a discussion about the nature of the equivalence, and perhaps its evolution, variation, and implications. – John Lawler Jul 5 '14 at 19:50
  • @ John, This is useful. Now I know which one I aim for. – wonderich Jul 5 '14 at 20:26
  • Another part of the answer is that you should use between when talking about two things, and among for three or more. – Scott Jul 5 '14 at 20:54
  • 1
    @Scott: I do not think you can say that as a definitive rule. See an earlier question – Henry Jul 5 '14 at 22:13
  • 3
    @Scott that rule smells like prescriptivist nonsense. These days they're probably effectively synonymous and I see no reason to make up rules for them. – curiousdannii Jul 6 '14 at 2:56

Grammatically and semantically, both options seem correct. Statistically, you're better off going with "of A and B".

A quick search on Google Scholar shows there are 141,000 occurrences of "equivalence of * and" and 59,600 occurrences of "equivalence between * and."

"Of" is roughly* 2.38 times more likely to be used in academic writing.

[* There is a fair amount of extrapolation since Google Scholar doesn't index the entire body of research out there, but there is no reason to assume it isn't a representative sample. ]

  • @ Guybrush Threepwood, thanks for the comment, +1. – wonderich Jul 24 '14 at 15:09

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