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I would like to ask how to make the following sentence better.

Let us denote the set of 3 apples, 2 bannas, and 4 cherries as A={a1, a2, a3}, B={b1, b2}, and C={c1, c2, c3, c4}, respectively, where a_k, b_k, and c_k represent the k-th apple, k-th banana, and k-th cherry, respectively.

Is this sentence good enough? If not, please tell me how to modify the sentence to be better.

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  • Being good enough is very subjective. I find it good. I made a small edit on the sentence. Let us denote the set of 3 apples, 2 bannas, and 4 cherries as A={a1, a2, a3}, B={b1, b2}, and C={c1, c2, c3, c4}, respectively. Where a_k, b_k, and c_k represent the k-th apple, k-th banana, and k-th cherry, respectively.
    – Codeformer
    Commented Jun 13, 2017 at 9:35
  • @Vinod Is it fine for a very formal paper if I use "~. Where ~" ? Do I have to write "~, where ~? But It is so awkward that I use two respectively in one sentence.
    – Danny_Kim
    Commented Jun 13, 2017 at 9:43
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    @Vinod Breaking it into two sentences that way leaves the second sentence dangling.
    – Lawrence
    Commented Jun 13, 2017 at 11:01
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    If you're just looking for good enough, you can drop both instances of respectively. Because the first instance already identifies the elements with the fruit, the second instance is not needed even if you're trying to be rigorous. Note, however, that you have 3 sets (plural). The set (singular) of 3 apples (first element), 2 bananas (second element) and 4 cherries (third element) would look like {A,B,C}, a set containing 3 elements.
    – Lawrence
    Commented Jun 13, 2017 at 11:03
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    In the first part, it helps to see 'respectively' to know what matches what. In the second part, you already say the fruit names, so 'respectively' no longer fits. Leave it out.
    – Yosef Baskin
    Commented Jun 13, 2017 at 11:07

1 Answer 1

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  1. 'Set' should be plural, as you are discussing 3 separate sets, not a single set containing 3 apples, 2 bananas, and 4 cherries.
  2. The second 'respectively' is not needed as you've already associated the item names (i.e. a_1) with the specific fruits.

I would note, however, that you have an opportunity to be more specific if you reword the second clause. For example, you could say something like the following:

Let us denote the sets of 3 apples, 2 bananas, and 4 cherries as A={a1, a2, a3}, B={b1, b2}, and C={c1, c2, c3, c4}, respectively, where the subscripts indicate the ordering of items within each set (i.e. a_k is the k-th apple).

Alternatively, you might mean something more like the following:

Let us denote the sets of 3 apples, 2 bananas, and 4 cherries as A={a1, a2, a3}, B={b1, b2}, and C={c1, c2, c3, c4}, respectively, where the subscripts indicate distinct items within each set.

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  • Another opportunity for clarity would be to split the two propositions into different sentences, viz. ... and C={c1, c2, c3, c4}, respectively. The subscripts indicate ...
    – John Lawler
    Commented Jun 13, 2017 at 14:50

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