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I am writing an article where I need to describe an equation like the one below, in reference to two mathematical objects, A and B, that I have already defined in the text.

f = #merge errors + #split errors

To do so, I need to define what merge and split errors are with respect to A and B.

One possibility is:

"A merge error refers to a pair of elements that were grouped in A, but not in B, and a split error refers to a pair of elements that were grouped in B, but not in A"

The above description is technically correct, but I would like to find a description that is less redundant (i.e. more compact). I thought of the following possibilities, but none of them sound correct to me:

"A merge error refers to a pair of elements that were grouped in A, but not in B, and a split error refers to the converse"

"A merge error refers to a pair of elements that were grouped in A, but not in B, and a split error is defined reciprocally"

"A merge error refers to a pair of elements that were grouped in A, but not in B, and a split error is defined conversely"

How can I define two objects where one is implicitly defined as the converse of the other?

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2 Answers 2

up vote 1 down vote accepted

The third sentence sounds most appropriate.

There is no difficulty though the terms are interdependent (defined reciprocally) -- it is still readable and clear enough.

Those familiar with the context can grasp your concept easily enough from the third sentence.

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The original sentence is better.

While it is less compact, it is clearer than any of the three alternatives. Redundancy is not a bad thing in this example: it ensures that the reader cannot possibly make a mistake in reading the definition, and the gain from eliminating redundancy is minimal here.

The two definitions also use exactly the same words "a pair of elements that were grouped in", which introduces symmetry between the two definitions and makes the sentence easier to read.

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