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I am just marking a couple of linear algebra papers in which one of the questions is to determine whether $(A+B)^2=A^2+2AB+B^2$ is true for 2-by-2 matrices or not. One of the students has chosen two numeric matrices one of which is double the other and concluded that the statement is true. I want to write something for her and I wonder which one of the following statements would describe the situation better:

You have chosen two specific matrices.

You have chosen two particular matrices.

Please consider that the question is not actually about what I should write for her or how I can help her and so on. The question is whether or not the words "specific" and "particular" are used interchangeably in mathematical (con)texts.

You can ignore this comment for now. I have an old interest in this question as you can see in this FLM paper and this ELU question.

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  • $\begingroup$ Instead of these comments, each of which says what the student did do, consider saying specifically what the student did not do: You have not shown the statement is true for any 2-by-2 matrices. (I would hope the question unambiguously asks whether the result is true for all 2-by-2 matrices. If not, then the questioner needs some "marking down" also!) $\endgroup$ – Dave L Renfro Jan 28 '16 at 18:39
  • $\begingroup$ Regarding your actual question, I only have a few moments so I'll just briefly remark that "specific" and "particular" are probably not entirely interchangable but I don't have a good example now. However, for your use here, "specific" sounds better to me but "particular" might sound better to someone else (i.e. I don't think there is much of a difference, if any). $\endgroup$ – Dave L Renfro Jan 28 '16 at 18:43
  • $\begingroup$ @DaveLRenfro I took that mark off from the questioner. That, in this case, happened to be me :) I wrote for the student, though not here, what she hasn't done. However, it is documented that they usually interpret "any" as "any of their own choice"! $\endgroup$ – Amir Asghari Jan 28 '16 at 19:35
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As a non-native speaker I'd tend towards particular in this context. Any 2x2 matrix would be a specific matrix, but the one used by the student was a particularly bad example.

Citing Merriam Webster:

[particular]: distinctive among other examples or cases of the same general category: notably unusual

To me, specific is "any fixed number/matrix/...", not neccessarily a special case, whereas particular always conveys some sort of "out-of-the-ordinary-ness". Example:

For any specific $\varepsilon$, one can find n such that...

vs.

For the particular $\varepsilon = 0.123$, it turns out to be n=123

"Any particular ..." doesn't sound right to me, but "any specific ..." does. So they are not always interchangeable.

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