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I am not sure whether "boundary" should be used in single form or plural form. For example, should I say:

I developed this method to define A region's boundary OR I developed this method to define the boundaries of A region


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Both are correct, with different implications. In the absence of constraints of context, you can use either. – Kris Dec 19 '12 at 4:41

"Boundary" designates the entire curve which encloses A; "boundaries" designates the several portions of that curve which respectively constitute the boundary between A and B, between A and C, between A and D, and so forth. So it seems to me the question is Which is more appropriate to your method?

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It depends on the nature of 'A region', but in some cases either boundary or boundaries can be used.

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