# Can we use "specific" and "particular" interchangeably all the time?

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.

• 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!) Commented Jan 28, 2016 at 18:39
• 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). Commented Jan 28, 2016 at 18:43
• @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"! Commented Jan 28, 2016 at 19:35

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.